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Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8

Go Math Answer Key: HMH Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8 are provided helps students to have learning targets and achieve success at chapter and lesson level and makes learning visible.

Download Go Math Answer Key for Grades K-8 | HMH Go Math Solution Key for Grades Kindergarten, 1, 2, 3, 4, 5, 6, 7, 8

All the Concepts in the CCSS Go Math Answer Key for Grades Kindergarten, 1, 2, 3, 4, 5, 6, 7, 8 are given with straightforward and detailed descriptions.

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Free Download Go Math Answer Key from Kindergarten to 8th Grade

Students can find Go Math Answer Keys right from Primary School to High School all in one place. You just need to tap on the quick links available in order to access them and learn all the Chapters in each grade. Once you tap on the quick link you will be directed to the respective Grade Solutions Key wherein you can access the complete information. You can find Solutions for all the Go Math Textbook Questions free of cost and we don’t charge any amount.

Go Math Kindergarten Answer Key

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Texas Go Math Kindergarten Answer Key

Go Math Grade K Answer Key

Chapter 1 Represent, Count, and Write Numbers 0 to 5
Chapter 2 Compare Numbers to 5
Chapter 3 Represent, Count, and Write Numbers 6 to 9
Chapter 4 Represent and Compare Numbers to 10
Chapter 5 Addition
Chapter 6 Subtraction
Chapter 7 Represent, Count, and Write 11 to 19
Chapter 8 Represent, Count, and Write 20 and Beyond
Chapter 9 Identify and Describe Two-Dimensional Shapes
Chapter 10 Identify and Describe Three-Dimensional Shapes
Chapter 11 Measurement
Chapter 12 Classify and Sort Data
Chapter 1 Addition Concepts
Chapter 2 Subtraction Concepts
Chapter 3 Addition Strategies
Chapter 4 Subtraction Strategies
Chapter 5 Addition and Subtraction Relationships
Chapter 6 Count and Model Numbers
Chapter 7 Compare Numbers
Chapter 8 Two-Digit Addition and Subtraction
Chapter 9 Measurement
Chapter 10 Represent Data
Chapter 11 Three-Dimensional Geometry
Chapter 12 Two-Dimensional Geometry
Chapter 1 Number Concepts
Chapter 2 Numbers to 1,000
Chapter 3 Basic Facts and Relationships
Chapter 4 2-Digit Addition
Chapter 5 2-Digit Subtraction
Chapter 6 3-Digit Addition and Subtraction
Chapter 7 Money and Time
Chapter 8 Length in Customary Units
Chapter 9 Length in Metric Units
Chapter 10 Data
Chapter 11 Geometry and Fraction Concepts

Grade 3 HMH Go Math – Answer Keys

Chapter 1: Addition and Subtraction within 1,000
Chapter 2: Represent and Interpret Data
Chapter 3: Understand Multiplication
Chapter 4: Multiplication Facts and Strategies
Chapter 5: Use Multiplication Facts
Chapter 6: Understand Division
Chapter 7: Division Facts and Strategies
Chapter 8: Understand Fractions
Chapter 9: Compare Fractions
Chapter 10: Time, Length, Liquid Volume, and Mass
Chapter 11: Perimeter and Area
Chapter 12:Two-Dimensional Shapes

Grade 3 HMH Go Math – Extra Practice Questions and Answers

Chapter 1: Addition and Subtraction within 1,000 Extra Practice
Chapter 2: Represent and Interpret Data Extra Practice
Chapter 3: Understand Multiplication Extra Practice
Chapter 4: Multiplication Facts and Strategies Extra Practice
Chapter 5: Use Multiplication Facts Extra Practice
Chapter 6: Understand Division Extra Practice
Chapter 7: Division Facts and Strategies Extra Practice
Chapter 8: Understand Fractions Extra Practice
Chapter 9: Compare Fractions Extra Practice
Chapter 10: Time, Length, Liquid Volume, and Mass Extra Practice
Chapter 11: Perimeter and Area Extra Practice
Chapter 12: Two-Dimensional Shapes Extra Practice

Common Core Grade 4 HMH Go Math – Answer Keys

Chapter 1 Place Value, Addition, and Subtraction to One Million
Chapter 2 Multiply by 1-Digit Numbers
Chapter 3 Multiply 2-Digit Numbers
Chapter 4 Divide by 1-Digit Numbers
Chapter 5 Factors, Multiples, and Patterns
Chapter 6 Fraction Equivalence and Comparison
Chapter 7 Add and Subtract Fractions
Chapter 8 Multiply Fractions by Whole Numbers
Chapter 9 Relate Fractions and Decimals
Chapter 10 Two-Dimensional Figures
Chapter 11 Angles
Chapter 12Relative Sizes of Measurement Units
Chapter 13 Algebra: Perimeter and Area

Grade 4 Homework Practice FL.

Common Core – Grade 4 – Practice Book

Chapter 1 Place Value, Addition, and Subtraction to One Million (Pages 1- 20)
Chapter 2 Multiply by 1-Digit Numbers (Pages 21 – 47)
Chapter 3 Multiply 2-Digit Numbers (Pages 49- 65)
Chapter 4 Divide by 1-Digit Numbers (Pages 67 – 93)
Chapter 5 Factors, Multiples, and Patterns (Pages 95 – 109)
Chapter 6 Fraction Equivalence and Comparison (Pages 111 – 129)
Chapter 7 Add and Subtract Fractions (Pages 131 – 153)
Chapter 8 Multiply Fractions by Whole Numbers (Pages 155- 167)
Chapter 9 Relate Fractions and Decimals (Pages 169- 185)
Chapter 10 Two-Dimensional Figures (Pages 187- 204)
Chapter 11 Angles (Pages 205- 217)
Chapter 12 Relative Sizes of Measurement Units (Pages 219- 244)
Chapter 13 Algebra: Perimeter and Area (Pages 245- 258)

Grade 4 Homework FL. – Answer Keys

Chapter 2 Multiply by 1-Digit Numbers Review/Test
Chapter 3 Multiply 2-Digit Numbers Review/Test
Chapter 4 Divide by 1-Digit Numbers Review/Test
Chapter 5 Factors, Multiples, and Patterns Review/Test
Chapter 6 Fraction Equivalence and Comparison Review/Test
Chapter 7 Add and Subtract Fractions Review/Test
Chapter 8 Multiply Fractions by Whole Numbers Review/Test
Chapter 9 Relate Fractions and Decimals Review/Test
Chapter 10 Two-Dimensional Figures Review/Test
Chapter 11 Angles Review/Test
Chapter 12 Relative Sizes of Measurement Units Review/Test
Chapter 13 Algebra: Perimeter and Area Review/Test
Chapter 1: Place Value, Multiplication, and Expressions
Chapter 2: Divide Whole Numbers
Chapter 3: Add and Subtract Decimals
Chapter 4: Multiply Decimals
Chapter 5: Divide Decimals
Chapter 6: Add and Subtract Fractions with Unlike Denominators
Chapter 7: Multiply Fractions
Chapter 8: Divide Fractions
Chapter 9: Algebra: Patterns and Graphing
Chapter 10: Convert Units of Measure
Chapter 11: Geometry and Volume
Chapter 1: Divide Multi-Digit Numbers
Chapter 2: Fractions and Decimals
Chapter 3: Understand Positive and Negative Numbers
Chapter 4: Model Ratios
Chapter 5: Model Percents
Chapter 6: Convert Units of Length
Chapter 7: Exponents
Chapter 8: Solutions of Equations
Chapter 9: Independent and Dependent Variables
Chapter 10: Area of Parallelograms
Chapter 11: Surface Area and Volume
Chapter 12: Data Displays and Measures of Center
Chapter 13: Variability and Data Distributions

Go Math Answer Key for Grade 7

Chapter 1: Adding and Subtracting Integers
Chapter 2: Multiplying and Dividing Integers
Chapter 3: Rational Numbers
Chapter 4: Rates and Proportionality
Chapter 5: Percent Increase and Decrease
Chapter 6: Algebraic Expressions
Chapter 7: Writing and Solving One-Step Inequalities
Chapter 8: Modeling Geometric Figures
Chapter 9: Circumference, Area, and Volume
Chapter 10: Random Samples and Populations
Chapter 11: Analyzing and Comparing Data
Chapter 12: Experimental Probability
Chapter 13: Theoretical Probability and Simulations
Chapter 1 Real Numbers
Chapter 2 Exponents and Scientific Notation
Chapter 3 Proportional Relationships
Chapter 4 Nonproportional Relationships
Chapter 5 Writing Linear Equations
Chapter 6 Functions
Chapter 7 Solving Linear Equations
Chapter 8 Solving Systems of Linear Equations
Chapter 9 Transformations and Congruence
Chapter 10 Transformations and Similarity
Chapter 11 Angle Relationships in Parallel Lines and Triangles
Chapter 12 The Pythagorean Theorem
Chapter 13 Volume
Chapter 14 Scatter Plots
Chapter 15 Two-Way Tables

Give your kid the right amount of knowledge he needs as a part of your preparation by taking the help of our HMH Go Math Answer Key for Grades K-8. Resolve all your queries and assess your preparation standard using the Common Core Go Math Solution Key.

Practicing from the Go Math Answer Key for Grades K to 8 will provide a grade by grade roadmap and prepares students for College Readiness. Gradewise HMH Go Math Answer Key provided will develop problem-solving skills among students thereby helping them to Think, Explore and Grow. The Diverse Opportunities provided helps Kids to master the content with engaging activities.

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All the Go Math Answer Key for Grades K to 8 are easy to download and we don’t charge any penny from you.
Step by Step Solutions provided in the HMH Go Math Practice Key is aligned as per the College and Career Expectations.
Solving from the Math 101 Practice Key helps you inculcate Higher Order Thinking Skills and you can answer any Question from your Homework, Assessment, or Review Test.
More Rigorous Content made available meets the Common Core State Standards Initiative.
You can gain a deeper knowledge of mathematical concepts and find solutions to all the Questions from Go Math Textbooks for Grades K, 1, 2, 3, 4, 5, 6, 7, 8

FAQs on Common Core HMH Go Math Answer Key

1. When Can I use the Go Math Answer Key for Grades K-8?

You can use the HMH Go Math Answer Key for Grades K to 8 while practicing the Go Math Textbook Questions as a part of your Homework or Assessment and make the most out of them.

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Yes, you can download the HMH Math 101 Practice Key for free on our page via quick links available and we don’t charge any amount for it.

Big Ideas Math Answers

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Engage NY Eureka Math Answer Key

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enVision Math Answer Key for Class 8, 7, 6, 5, 4, 3, 2, 1, and K | enVisionmath 2.0 Common Core Grades K-8

Envision math common core answer key for grade 8, 7, 6, 5, 4, 3, 2, 1, and k.

enVision Math Common Core Kindergarten Answer Key

enVision Math Common Core Grade 1 Answer Key

Envision math common core grade 2 answer key, envision math common core grade 3 answer key, envision math common core grade 4 answer key, envision math common core grade 5 answer key, envision math common core grade 6 answer key, envision math common core grade 7 answer key, envision math common core grade 8 answer key.

Common Core Resources

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Topic 1 Real Numbers
Topic 2 Analyze and Solve Linear Equations
Topic 3 Use Functions to Model Relationships
Topic 4 Investigate Bivariate Data
Topic 5 Analyze and Solve Systems of Linear Equations
Topic 6 Congruence and Similarity
Topic 7 Understand and Apply the Pythagorean Theorem
Topic 8 Solve Problems Involving Surface Area and Volume
Topic 1 Rational Number Operations
Topic 2 Analyze and Use Proportional Relationships
Topic 3 Analyze and Solve Percent Problems
Topic 4 Generate Equivalent Expressions
Topic 5 Solve Problems Using Equations and Inequalities
Topic 6 Use Sampling to Draw Inferences About Populations
Topic 7 Probability
Topic 8 Solve Problems Involving Geometry
Topic 1 Use Positive Rational Numbers
Topic 2 Integers and Rational Numbers
Topic 3 Numeric and Algebraic Expressions
Topic 4 Represent and Solve Equations and Inequalities
Topic 5 Understand and Use Ratio and Rate
Topic 6 Understand and Use Percent
Topic 7 Solve Area, Surface Area, and Volume Problems
Topic 8 Display, Describe and Summarize Data
Topic 1 Understand Place Value
Topic 2 Use Models and Strategies to Add and Subtract Decimals
Topic 3 Fluently Multiply Multi-Digit Whole Numbers
Topic 4 Use Models and Strategies to Multiply Decimals
Topic 5 Use Models and Strategies to Divide Whole Numbers
Topic 6 Use Models and Strategies to Divide Decimals
Topic 7 Use Equivalent Fractions to Add and Subtract Fractions
Topic 8 Apply Understanding of Multiplication to Multiply Fractions
Topic 9 Apply Understanding of Division to Divide Fractions
Topic 10 Represent and Interpret Data
Topic 11 Understand Volume Concepts
Topic 12 Convert Measurements
Topic 13 Write and Interpret Numerical Expressions
Topic 14 Graph Points on the Coordinate Plane
Topic 15 Algebra: Analyze Patterns and Relationships
Topic 16 Geometric Measurement: Classify Two-Dimensional Figures
Topic 1 Generalize Place Value Understanding
Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers
Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers
Topic 4 Use Strategies and Properties to Multiply by 2-Digit Numbers
Topic 5 Use Strategies and Properties to Divide by 1-Digit Numbers
Topic 6 Use Operations with Whole Numbers to Solve Problems
Topic 7 Factors and Multiples
Topic 8 Extend Understanding of Fraction Equivalence and Ordering
Topic 9 Understand Addition and Subtraction of Fractions
Topic 10 Extend Multiplication Concepts to Fractions
Topic 11 Represent and Interpret Data on Line Plots
Topic 12 Understand and Compare Decimals
Topic 13 Measurement: Find Equivalence in Units of Measure
Topic 14 Algebra: Generate and Analyze Patterns
Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement
Topic 16 Lines, Angles, and Shapes
Topic 1 Understand Multiplication and Division of Whole Numbers
Topic 2 Multiplication Facts: Use Patterns
Topic 3 Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8
Topic 4 Use Multiplication to Divide: Division Facts
Topic 5 Fluently Multiply and Divide within 100
Topic 6 Connect Area to Multiplication and Addition
Topic 7 Represent and Interpret Data
Topic 8 Use Strategies and Properties to Add and Subtract
Topic 9 Fluently Add and Subtract within 1,000
Topic 10 Multiply by Multiples of 10
Topic 11 Use Operations with Whole Numbers to Solve Problems
Topic 12 Understand Fractions as Numbers
Topic 13 Fraction Equivalence and Comparison
Topic 14 Solve Time, Capacity, and Mass Problems
Topic 15 Attributes of Two-Dimensional Shapes
Topic 16 Solve Perimeter Problems
Topic 1 Fluently Add and Subtract Within 20
Topic 2 Work with Equal Groups
Topic 3 Add Within 100 Using Strategies
Topic 4 Fluently Add Within 100
Topic 5 Subtract Within 100 Using Strategies
Topic 6 Fluently Subtract Within 100
Topic 7 More Solving Problems Involving Addition and Subtraction
Topic 8 Work with Time and Money
Topic 9 Numbers to 1,000
Topic 10 Add Within 1,000 Using Models and Strategies
Topic 11 Subtract Within 1,000 Using Models and Strategies
Topic 12 Measuring Length
Topic 13 Shapes and Their Attributes
Topic 14 More Addition, Subtraction, and Length
Topic 15 Graphs and Data
Topic 1 Understand Addition and Subtraction
Topic 2 Fluently Add and Subtract Within 10
Topic 3 Addition Facts to 20: Use Strategies
Topic 4 Subtraction Facts to 20: Use Strategies
Topic 5 Work with Addition and Subtraction Equations
Topic 6 Represent and Interpret Data
Topic 7 Extend the Counting Sequence
Topic 8 Understand Place Value
Topic 9 Compare Two-Digit Numbers
Topic 10 Use Models and Strategies to Add Tens and Ones
Topic 11 Use Models and Strategies to Subtract Tens
Topic 12 Measure Lengths
Topic 13 Time and Money
Topic 14 Reason with Shapes and Their Attributes
Topic 15 Equal Shares of Circles and Rectangles

enVision Math Common Core Grade K Answer Key

Topic 1 Numbers 0 to 5
Topic 2 Compare Numbers 0 to 5
Topic 3 Numbers 6 to 10
Topic 4 Compare Numbers 0 to 10
Topic 5 Classify and Count Data
Topic 6 Understand Addition
Topic 7 Understand Subtraction
Topic 8 More Addition and Subtraction
Topic 9 Count Numbers to 20
Topic 10 Compose and Decompose Numbers 11 to 19
Topic 11 Count Numbers to 100
Topic 12 Identify and Describe Shapes
Topic 13 Analyze, Compare, and Create Shapes
Topic 14 Describe and Compare Measurable Attributes

Mr. Math Blog

Convert Units of Length - Lesson 6.1

Convert Units of Capacity - Lesson 6.2

Convert Units of Weight and Mass - Lesson 6.3

Transform Units - Lesson 6.4

Problem Solving - Distance, Rate, and Time - Lesson 6.5

Fractions and Decimals - Lesson 2.1

Compare and order Fractions and Decimals - Lesson 2.2

Multiply Fractions - Lesson 2.3

Simplify Factors - Lesson 2.4

Model Fraction Division - Lesson 2.5

Estimate Quotients - Lesson 2.6

Dividing Fractions - Lesson 2.7

Model Mixed Number Division - Lesson 2.8

Divide Mixed Numbers - Lesson 2.9

Problem Solving - Fraction Operations - Lesson 2.10

Understanding Positive and Negative Integers - Lesson 3.1

Compare and Order Integers - Lesson 3.2

Rational Numbers and the Number Line - Lesson 3.3

Compare and Order Rational Numbers - Lesson 3.4

Absolute Value - Lesson 3.5

Compare Absolute Value - Lesson 3.6

Rational Numbers and the Coordinate Plane - Lesson 3.7

Ordered Pair Relationships - Lesson 3.8

Distance on the Coordinate Plane - Lesson 3.9

Problem Solving - The Coordinate Plane - Lesson 3.10

Solutions of Equations - Lesson 8.1

Writing Equations - Lesson 8.2

Model and Solve Addition Equations - Lesson 8.3

Solve Addition & Subtraction Equations - Lesson 8.4

Sixth Grade

Math

Model Ratios - Lesson 4.1

Ratios and Rates - Lesson 4.2

Equivalent Ratios and the Multiplication Table - Lesson 4.3

Use Tables to Compare Ratios - Lesson 4.4

Use Equivalent Ratios - Lesson 4.5

Find Unit Rates - Lesson 4.6

Use Unit Rates - Lesson 4.7

Equivalent Ratios and Graphs - Lesson 4.8

Three Dimensional Figures and Nets - Lesson 11.1

Surface Area of Prisms - Lesson 11.3

Surface Area of Pyramids - Lesson 11.4

Volume of a Rectangular Prism - Lesson 11.6

Area of Parallelograms - Lesson 10.1

Explore Area of Triangles - Lesson 10.2

Area of Triangles - Lesson 10.3

Explore Area of Trapezoids - Lesson 10.4

Area of Trapezoids - Lesson 10.5

Area of Regular Polygons - Lesson 10.6

Composite Figures - Lesson 10.7

Divide Multi-Digit Numbers - Lesson 1.1

Prime Factorization - Lesson 1.2

Least Common Multiple (LCM) - Lesson 1.3

Greatest Common Factor (GCF) - Lesson 1.4

Problem Solving: Apply the GCF - Lesson 1.5

Add and Subtract Decimals - Lesson 1.6

Multiply Decimals - Lesson 1.7

Divide Decimals by Whole Numbers - Lesson 1.8

Divide with Decimals - Lesson 1.9

Chapter 1 Review for Test

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Exponents - Lesson 7.1

Evaluating Expressions Involving Exponents - Lesson 7.2

Write Algebraic Expressions - Lesson 7.3

Identify Parts of Expressions - Lesson 7.4

Evaluate Algebraic Expressions and Formulas - Lesson 7.5

Use Algebraic Expressions - Lesson 7.6

Problem Solving - Combining Like Terms - Lesson 7.7

Generate Equivalent Expressions - Lesson 7.8

Identify Equivalent Expressions - Lesson 7.9

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Independent and Dependent Variables - Lesson 9.1

Equations and Tables - Lesson 9.2

Model Percents - Lesson 5.1

Write Percents as Fractions and Decimals - Lesson 5.2

Write Fractions and Decimals as Percents - Lesson 5.3

Percent of a Quantity - Lesson 5.4

Problem Solving - Percents - Lesson 5.5

Find the Whole From a Percent - Lesson 5.6

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Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals

Are you looking for the best material to score top in the exams? Then, you are in the right place. HMH Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals is the best material for the 6th standard students. Here you can find the explanations for each and every question in different methods. Refer to Go Math Grade 6 Chapter 2 Fractions and Decimals Solution Key to learn the concepts of the chapter. So, Download HMH Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals for free.

Download Go Math Grade 6 Chapter 2 Fractions and Decimals Answer Key PDF

The Go Math Grade 6 Chapter 2 Fractions and Decimals Solution Key consists of various topics like compare and order fractions and decimals, multiply fractions, Divide Fractions, Model Mixed Number Division, etc. We have provided detailed explanations in simple methods here. All the solutions are prepared according to the topics in the Fractions and Decimals Chapter. So, access the links and start your preparation for the exams.

Lesson 1: Fractions and Decimals

Fractions and Decimals – Page No. 71
Fractions and Decimals – Page No. 72
Fractions and Decimals Lesson Check – Page No. 73
Fractions and Decimals Lesson Check 1 – Page No. 74

Lesson 2: Compare and Order Fractions and Decimals

Compare and Order Fractions and Decimals – Page No. 77
Compare and Order Fractions and Decimals – Page No. 78
Compare and Order Fractions and Decimals Lesson Check – Page No. 79
Compare and Order Fractions and Decimals Lesson Check 1 – Page No. 80

Lesson 3: Multiply Fractions

Multiply Fractions – Page No. 83
Multiply Fractions – Page No. 84
Multiply Fractions Lesson Check – Page No. 85
Multiply Fractions Lesson Check 1 – Page No. 86

Lesson 4: Simplify Factors

Simplify Factors – Page No. 89
Simplify Factors – Page No. 90
Simplify Factors Lesson Check – Page No. 91
Simplify Factors Lesson Check 1 – Page No. 92

Mid-Chapter Checkpoint

Mid-Chapter Checkpoint – Page No. 93
Mid-Chapter Checkpoint Lesson Check – Page No. 94

Lesson 5: Investigate • Model Fraction Division

Model Fraction Division – Page No. 97
Model Fraction Division – Page No. 98
Model Fraction Division Lesson Check – Page No. 99
Model Fraction Division Lesson Check 1 – Page No. 100

Lesson 6: Estimate Quotients

Estimate Quotients – Page No. 103
Estimate Quotients – Page No. 104
Estimate Quotients Lesson Check – Page No. 105
Estimate Quotients Lesson Check 1 – Page No. 106

Lesson 7: Divide Fractions

Divide Fractions – Page No. 109
Divide Fractions – Page No. 110
Divide Fractions Lesson Check – Page No. 111
Divide Fractions Lesson Check 1 – Page No. 112

Lesson 8: Investigate • Model Mixed Number Division

Model Mixed Number Division – Page No. 115
Model Mixed Number Division – Page No. 116
Model Mixed Number Division Lesson Check – Page No. 117
Model Mixed Number Division Lesson Check 1 – Page No. 118

Lesson 9: Divide Mixed Numbers

Divide Mixed Numbers – Page No. 121
Divide Mixed Numbers – Page No. 122
Divide Mixed Numbers Lesson Check – Page No. 123
Divide Mixed Numbers Lesson Check 1– Page No. 124

Lesson 10: Problem Solving • Fraction Operations

Fraction Operations – Page No. 127
Fraction Operations – Page No. 128
Fraction Operations Lesson Check – Page No. 129
Fraction Operations Lesson Check 1– Page No. 130

Chapter 2 Review/Test

Review/Test – Page No. 131
Review/Test – Page No. 132
Review/Test – Page No. 133
Review/Test – Page No. 134
Review/Test – Page No. 135
Review/Test – Page No. 136

Share and Show – Page No. 71

Write as a fraction or as a mixed number in simplest form.

Question 1. 95.5 _____ $\frac{□}{□}$

Answer: $\frac{1}{2}$

Explanation: 95.5 95.5 is 95 ones and 5 tenths. 5 tenths = $\frac{5}{10}$ Simplify using the GCF. The GCF of 5 and 10 is 10. Divide the numerator and the denominator by 10 $\frac{5 ÷ 10}{10 ÷ 10}$ = $\frac{1}{2}$

Question 2. 0.6 $\frac{□}{□}$

Answer: $\frac{3}{5}$

Explanation: 0.6 6 tenths = $\frac{6}{10}$ Simplify using the GCF. The GCF of 6 and 10 is 2. Divide the numerator and the denominator by 10 $\frac{6 ÷ 2}{10 ÷ 2}$ = $\frac{3}{5}$

Question 3. 5.75 _____ $\frac{□}{□}$

Answer: 5$\frac{3}{4}$

Explanation: 5.75 is 5 ones and 75 hundredths. 75 hundredths = $\frac{75}{100}$ Simplify using the GCF. The GCF of 75 and 100 is 25. Divide the numerator and the denominator by 25 5$\frac{75 ÷ 25}{100 ÷ 25}$ = 5$\frac{3}{4}$

Write as a decimal.

Question 4. $\frac{7}{8}$ _____

Answer: 0.875

Explanation: Use division to rename the fraction part as a decimal. 7/8 = 0.875 The quotient has 3 decimal places. Add the whole number to the decimal. 0 + 0.875 = 0.875. So, $\frac{7}{8}$ = 0.875

Question 5. $\frac{13}{20}$ _____

Answer: 0.65

Explanation: Use division to rename the fraction part as a decimal. $\frac{13}{20}$ = 0.65 The quotient has 2 decimal places. Add the whole number to the decimal. 0 + 0.65 = 0.65. So, $\frac{13}{20}$ = 0.65

Question 6. $\frac{3}{25}$ _____

Answer: 0.12

Explanation: Use division to rename the fraction part as a decimal. $\frac{3}{25}$ = 0.12 The quotient has 2 decimal places. Add the whole number to the decimal. 0 + 0.12 = 0.12. So, $\frac{3}{25}$= 0.12

On Your Own

Question 7. 0.27 $\frac{□}{□}$

Answer: $\frac{27}{100}$

Explanation: 0.27 is 0 ones and 27 hundredths. 27 hundredths = $\frac{27}{100}$ Simplify using the GCF. The GCF of 27 and 100 is 1. Divide the numerator and the denominator by 1 $\frac{27 ÷ 1}{100 ÷ 1}$ = $\frac{27}{100}$

Question 8. 0.055 $\frac{□}{□}$

Answer: $\frac{11}{200}$

Explanation: 0.055 is 0 ones and 55 thousandths. 55 thousandths = $\frac{55}{1000}$ Simplify using the GCF. The GCF of 55 and 1000 is 5. Divide the numerator and the denominator by 5 $\frac{55 ÷ 5}{1000 ÷ 5}$ = $\frac{11}{200}$

Question 9. 2.45 _____ $\frac{□}{□}$

Answer: $\frac{9}{20}$

Explanation: 2.45 is 2 ones and 45 hundredths. 45 hundredths = $\frac{45}{100}$ Simplify using the GCF. The GCF of 45 and 100 is 5. Divide the numerator and the denominator by 1 $\frac{45 ÷ 5}{100 ÷ 5}$ = $\frac{9}{20}$

Question 10. $\frac{3}{8}$ _____

Answer: 0.375

Explanation: Use division to rename the fraction part as a decimal. $\frac{3}{8}$ = 0.375 The quotient has 3 decimal places. Add the whole number to the decimal. 0 + 0.375 = 0.375. So, $\frac{3}{8}$ = 0.375

Question 11. 3 $\frac{1}{5}$ _____

Answer: 3.2

Explanation: Use division to rename the fraction part as a decimal. $\frac{1}{5}$ = 0.2 The quotient has 1 decimal place. Add the whole number to the decimal. 3 + 0.2 = 3.2. So, 3 $\frac{1}{5}$ = 3.2

Question 12. 2 $\frac{11}{20}$ _____

Answer: 2.55

Explanation: Use division to rename the fraction part as a decimal. $\frac{11}{20}$ = 0.55 The quotient has 2 decimal places. Add the whole number to the decimal. 2 + 0.55 = 2.55. So, 2 $\frac{11}{20}$ = 2.55

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 1$

Question 13. Point A Type below: __________

Answer: 0.2

Question 14. Point B Type below: __________

Answer: 0.9

Explanation: Point B is between 0.8 and 1.0. Every point is separated by 0.1. So, Point B is at 0.9

Question 15. Point C Type below: __________

Answer: 0.5

Explanation: Point C is between 0.4 and 0.6. Every point is separated by 0.1. So, Point C is at 0.5

Question 16. Point D Type below: __________

Answer: 0.1

Explanation: Point D is between 0 and 0.2. Every point is separated by 0.1. So, Point D is at 0.1

Problem Solving + Applications – Page No. 72

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 2$

Question 17. Members of the Ozark Trail Hiking Club hiked a steep section of the trail in June and July. The table shows the distances club members hiked in miles. Write Maria’s July distance as a decimal. _____ miles

Answer: 2.625 miles

Explanation: Maria’s July distance = 2 $\frac{5}{8}$ Use division to rename the fraction part as a decimal. $\frac{5}{8}$ = 0.625 The quotient has 3 decimal places. Add the whole number to the decimal. 2 + 0.625 = 2.625. 2 $\frac{5}{8}$ = 2.625

Question 18. How much farther did Zoey hike in June and July than Maria hiked in June and July? Explain how you found your answer. _____ miles

Answer: 0.7 miles

Explanation: Maria: June = 2.95, July = 2 $\frac{5}{8}$ = 2.58 Zoey: June = 2.85, July = 3 $\frac{3}{8}$ = 3.38 [2.85 + 3.38] – [2.95 + 2.58] = 0.7 miles

Question 19. What’s the Error? Tabitha’s hiking distance in July was 2 $\frac{1}{5}$ miles. She wrote the distance as 2.02 miles. What error did she make? Type below: __________

Answer: Tabitha’s hiking distance in July was 2 $\frac{1}{5}$ miles. 2 $\frac{1}{5}$ Use division to rename the fraction part as a decimal. $\frac{1}{5}$ = 0.2 The quotient has 1 decimal place. Add the whole number to the decimal. 2 + 0.2 = 2.2. 2 $\frac{1}{5}$ = 2.2 She wrote the distance as 2.02 miles in mistake.

Question 20. Use Patterns Write $\frac{3}{8}, \frac{4}{8}, \text { and } \frac{5}{8}$ as decimals. What pattern do you see? Use the pattern to predict the decimal form of $\frac{6}{8}$ and $\frac{7}{8}$. Type below: __________

Answer: $\frac{3}{8}, \frac{4}{8}, \text { and } \frac{5}{8}$ as decimals. 0.375, 0.5, 0.625 Each decimal is separated by 0.125. So, 6/8 = 0.625 + 0.125 = 0.75 7/8 = 0.75 + 0.125 = 0.875

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 3$

Answer: Point A: 0.5 Point B: 0.7 Point C: 0.3 Point D: 0.8

Explanation: Every point is differentiated by 0.1 distance. The A is between 0.4 and 0.6 which is 0.5 The B is between 0.6 and 0.8 which is 0.7 The C is between 0.1 and 0.6 which is 0.53

Fractions and Decimals – Page No. 73

Question 1. 0.52 $\frac{□}{□}$

Answer: $\frac{13}{25}$

Explanation: 0.52 0.52 is 52 hundredths. 52 hundredths = $\frac{52}{100}$ Simplify using the GCF. The GCF of 52 and 100 is 4. Divide the numerator and the denominator by 4 $\frac{52 ÷ 4}{100 ÷ 4}$ = $\frac{13}{25}$

Question 2. 0.02 $\frac{□}{□}$

Answer: $\frac{1}{50}$

Explanation: 0.02 0.02 is 2 hundredths. 2 hundredths = $\frac{2}{100}$ Simplify using the GCF. The GCF of 2 and 100 is 2. Divide the numerator and the denominator by 2 $\frac{2 ÷ 2}{100 ÷ 2}$ = $\frac{1}{50}$

Question 3. 4.8 ______ $\frac{□}{□}$

Answer: $\frac{4}{5}$

Explanation: 4.8 4.8 is 4 ones and 8 tenths. 8 tenths = $\frac{8}{10}$ Simplify using the GCF. The GCF of 8 and 10 is 2. Divide the numerator and the denominator by 2 $\frac{8 ÷ 2}{10 ÷ 2}$ = $\frac{4}{5}$

Question 4. 6.025 ______ $\frac{□}{□}$

Answer: $\frac{1}{40}$

Explanation: 6.025 is 6 ones and 25 thousandths. 25 thousandths = $\frac{25}{1000}$ Simplify using the GCF. The GCF of 25 and 1000 is 25. Divide the numerator and the denominator by 25 $\frac{25 ÷ 25}{1000 ÷ 25}$ = $\frac{1}{40}$

Question 5. $\frac{17}{25}$ ______

Answer: 0.68

Explanation: Use division to rename the fraction part as a decimal. 17/25 = 0.68 The quotient has 2 decimal places. Add the whole number to the decimal. 0 + 0.68 = 0.68. So, $\frac{17}{25}$ = 0.68

Question 6. $\frac{11}{20}$ ______

Answer: 0.55

Explanation: Use division to rename the fraction part as a decimal. 11/20 = 0.55 The quotient has 2 decimal places. Add the whole number to the decimal. 0 + 0.55 = 0.55. So, $\frac{11}{20}$ = 0.55

Question 7. 4 $\frac{13}{20}$ ______

Answer: 4.65

Explanation: Use division to rename the fraction part as a decimal. $\frac{13}{20}$ = 0.65 The quotient has 2 decimal places. Add the whole number to the decimal. 4 + 0.65 = 4.65. So, 4 $\frac{13}{20}$ = 4.65

Question 8. 7 $\frac{3}{8}$ ______

Answer: 7.375

Explanation: Use division to rename the fraction part as a decimal. $\frac{3}{8}$ = 0.375 The quotient has 3 decimal places. Add the whole number to the decimal. 7 + 0.375 = 7.375. So, 7 $\frac{3}{8}$ = 7.375

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 4$

Question 9. Point A Type below: __________

Answer: 0.4

Explanation:

Point A is between 0 and 0.5. Every point is separated by 0.1. So, Point A is at 0.4

Question 10. Point D Type below: __________

Answer: 1.9

Explanation: Point D is between 1.5 and 2. Every point is separated by 0.1. So, Point D is at 1.9

Question 11. Point C Type below: __________

Answer: 1.2

Explanation: Point C is between 1 and 1.5. Every point is separated by 0.1. So, Point C is at 1.2

Question 12. Point B Type below: __________

Answer: 0.6

Explanation: Point C is between 0.5 and 1. Every point is separated by 0.1. So, Point C is at 0.6

Problem Solving

Question 13. Grace sold $\frac{5}{8}$ of her stamp collection. What is this amount as a decimal? ______

Answer: 0.625

Explanation: Grace sold $\frac{5}{8}$ of her stamp collection. Use division to rename the fraction part as a decimal. $\frac{5}{8}$ = 0.625 The quotient has 3 decimal places. Add the whole number to the decimal. 0 + 0.625 = 0.625. So, $\frac{5}{8}$ = 0.625

Question 14. What if you scored an 0.80 on a test? What fraction of the test, in simplest form, did you answer correctly? $\frac{□}{□}$

Explanation: 0.80 is 0 ones and 8 tenths. 8 tenths = $\frac{8}{10}$ Simplify using the GCF. The GCF of 8 and 10 is 2. Divide the numerator and the denominator by 2 $\frac{8 ÷ 2}{10 ÷ 2}$ = $\frac{4}{5}$

Question 15. What fraction in simplest form is equivalent to 0.45? What decimal is equivalent to $\frac{17}{20}$? Explain how you found your answers. Type below: __________

Answer: 0.45 is 0 ones and 45 hundredths. 45 hundredths = $\frac{45}{100}$ Simplify using the GCF. The GCF of 45 and 100 is 5. Divide the numerator and the denominator by 5 $\frac{45 ÷ 5}{100 ÷ 5}$ = $\frac{9}{20}$ $\frac{17}{20}$ Use division to rename the fraction part as a decimal. $\frac{17}{20}$ = 0.85 The quotient has 2 decimal places. Add the whole number to the decimal. 0 + 0.85 = 0.85. So, $\frac{17}{20}$ = 0.85

Lesson Check – Page No. 74

Question 1. After a storm, Michael measured 6 $\frac{7}{8}$ inches of snow. What is this amount as a decimal? ______ inches

Answer: 6.875 inches

Explanation: Michael measured 6 $\frac{7}{8}$ inches of snow. Use division to rename the fraction part as a decimal. $\frac{7}{8}$ = 0.875 The quotient has 3 decimal places. Add the whole number to the decimal. 6 + 0.875 = 6.875. So, 6 $\frac{7}{8}$ = 6.875.

Question 2. A recipe calls for 3.75 cups of flour. What is this amount as a mixed number in simplest form? ______ $\frac{□}{□}$ cups

Answer: 3 $\frac{3}{4}$ cups

Explanation: A recipe calls for 3.75 cups of flour. 3 + 0.75 0.75 is 0 ones and 75 hundredths. 75 hundredths = $\frac{75}{100}$ Simplify using the GCF. The GCF of 75 and 100 is 25. Divide the numerator and the denominator by 25 $\frac{75 ÷ 25}{100 ÷ 25}$ = $\frac{3}{4}$ 3 $\frac{3}{4}$

Spiral Review

Question 3. Gina bought 2.3 pounds of red apples and 2.42 pounds of green apples. They were on sale for $0.75 a pound. How much did the apples cost altogether? $ ______

Answer: $3.54

Explanation: Gina bought 2.3 pounds of red apples and 2.42 pounds of green apples. They were on sale for $0.75 a pound. $0.75 x 2.3 = 1.725 $0.75 x 2.42 = 1.815 1.725 + 1.815 = 3.54 So the apples cost $3.54

Question 4. Ken has 4.66 pounds of walnuts, 2.1 pounds of cashews, and 8 pounds of peanuts. He mixes them together and divides them equally among 18 bags. How many pounds of nuts are in each bag? ______ pounds

Answer: 0.82 pounds

Explanation: Ken has 4.66 pounds of walnuts, 2.1 pounds of cashews, and 8 pounds of peanuts. 4.66 + 2.1 + 8 = 14.76 He mixes them together and divides them equally among 18 bags. 14.76/18 = 0.82

Question 5. Mia needs to separate 270 blue pens and 180 red pens into packs. Each pack will have the same number of blue pens and the same number of red pens. What is the greatest number of packs she can make? How many red pens and how many blue pens will be in each pack? Type below: __________

Answer: There are 2 red pens and 3 blue pens in each pack.

Explanation: Mia needs to separate 270 blue pens and 180 red pens into packs. The GCF of 270 and 180 is 90 The greatest number of packs she can make is 90. Divide the total number of red pens by the total number of packs. 180/90 = 2 Divide the total number of blue pens by the total number of packs. 270/90 = 3 There are 2 red pens and 3 blue pens in each pack.

Question 6. Evan buys 19 tubes of watercolor paint for $50.35. What is the cost of each tube of paint? $ ______

Answer: $2.65

Explanation: Evan buys 19 tubes of watercolor paint for $50.35. $50.35/19 = $2.65

Share and Show – Page No. 77

Order from least to greatest.

Question 1. $3 \frac{3}{6}, 3 \frac{5}{8}, 2 \frac{9}{10}$ Type below: __________

Answer: 2 $\frac{9}{10}$ < 3 $\frac{3}{6}$ < 3 $\frac{5}{8}$

Explanation: $3 \frac{3}{6}, 3 \frac{5}{8}, 2 \frac{9}{10}$ Compare the whole numbers first. 2 < 3 If the whole numbers are the same, compare the fractions. 3 $\frac{3}{6}$, 3 $\frac{5}{8}$ 6 and 8 are multiples of 48. So, 48 is a common denominator. 3 $\frac{3 x 8}{6 x 8}$ = 3 $\frac{24}{48}$, 3 $\frac{5 x 6}{8 x 6}$ = 3 $\frac{30}{48}$ 3 $\frac{24}{48}$ < 3 $\frac{30}{48}$ So, 3 $\frac{3}{6}$ < 3 $\frac{5}{8}$ Order the fractions from least to greatest. 2 $\frac{9}{10}$ < 3 $\frac{3}{6}$ < 3 $\frac{5}{8}$

Write <, >, or =.

Question 2. 0.8 _____ $\frac{4}{12}$

Answer: 0.8 < latex]\frac{4}{12}[/latex]

Explanation: Write the decimal form of $\frac{4}{12}$ = 0.3333 0.8 > 0.333 So, 0.8 < latex]\frac{4}{12}[/latex]

Question 3. 0.22 _____ $\frac{1}{4}$

Answer: 0.22 < $\frac{1}{4}$

Explanation: Write the decimal form of $\frac{1}{4}$ = 0.25 0.22 < 0.25 So, 0.22 < $\frac{1}{4}$

Question 4. $\frac{1}{20}$ _____ 0.06

Answer: $\frac{1}{20}$ < 0.06

Explanation: Write the decimal form of $\frac{1}{20}$ = 0.05 0.05 < 0.06 So, $\frac{1}{20}$ < 0.06

Use a number line to order from least to greatest.

Question 5. $1 \frac{4}{5}, 1.25, 1 \frac{1}{10}$ Type below: __________

Answer: 1$\frac{1}{10}$, 1.25, 1$\frac{4}{5}$

Explanation: Write the decimal form of 1$\frac{4}{5}$ = 1.8 Write the decimal form of 1$\frac{1}{10}$ = 1.1 1.8, 1.25, 1.1 Locate each decimal on a number line. So, from least to greatest, the order is 1.1, 1.25, 1.8 1$\frac{1}{10}$, 1.25, 1$\frac{4}{5}$

Question 6. 0.6, $\frac{4}{5}$, 0.75 Type below: __________

Answer: 0.6, 0.75, $\frac{4}{5}$

Explanation: Write the decimal form of $\frac{4}{5}$ = 0.8 0.6, 0.8, 0.75 Compare decimals. All ones are equal. Compare tenths: 6 < 7 < 8 So, from least to greatest, the order is 0.6, 0.75, 0.8 So, 0.6, 0.75, $\frac{4}{5}$

Question 7. $\frac{1}{2}$, $\frac{2}{5}$, $\frac{7}{15}$ Type below: __________

Answer: $\frac{2}{5}$, $\frac{7}{15}$, $\frac{1}{2}$

Explanation: Write the decimal form of $\frac{1}{2}$ = 0.5 Write the decimal form of $\frac{2}{5}$ = 0.4 Write the decimal form of $\frac{7}{15}$ = 0.466 0.5, 0.4, 0.466 Compare decimals. All ones are equal. Compare tenths: 4 < 5 Compare hundredths of 0.4 and 0.466; 0 < 6 So, from least to greatest, the order is 0.4 < 0.466 < 0.5 So, $\frac{2}{5}$, $\frac{7}{15}$, $\frac{1}{2}$

Question 8. 5 $\frac{1}{2}$, 5.05, 5 $\frac{5}{9}$ Type below: __________

Answer: 5.05, 5 $\frac{1}{2}$, 5 $\frac{5}{9}$

Explanation: Write the decimal form of 5 $\frac{1}{2}$ = 5.5 Write the decimal form of 5 $\frac{5}{9}$ = 5.555 5.5, 5.05, 5.5555 Compare decimals. All ones are equal. Compare tenths: 0 < 5 Compare hundredths of 5.5 and 5.55; 0 < 5 So, from least to greatest, the order is 5.05 < 5.5 < 5.55 So, 5.05, 5 $\frac{1}{2}$, 5 $\frac{5}{9}$

Question 9. $\frac{5}{7}$, $\frac{5}{6}$, $\frac{5}{12}$ Type below: __________

Answer: $\frac{5}{12}$, $\frac{5}{7}$, $\frac{5}{6}$

Explanation: $\frac{5}{7}$, $\frac{5}{6}$, $\frac{5}{12}$ To compare fractions with the same numerators, compare the denominators. So, from least to greatest, the order is $\frac{5}{12}$, $\frac{5}{7}$, $\frac{5}{6}$

Question 10. $\frac{7}{15}$ _____ $\frac{7}{10}$

Answer: $\frac{7}{15}$ < $\frac{7}{10}$

Explanation: $\frac{7}{15}$ and $\frac{7}{10}$ To compare fractions with the same numerators, compare the denominators. So, $\frac{7}{15}$ < $\frac{7}{10}$

Question 11. $\frac{1}{8}$ _____ 0.125

Answer: $\frac{1}{8}$ = 0.125

Explanation: Write the decimal form of $\frac{1}{8}$ = 0.125 0.125 = 0.125

Question 12. 7 $\frac{1}{3}$ _____ 6 $\frac{2}{3}$

Answer: 7 $\frac{1}{3}$ > 6 $\frac{2}{3}$

Explanation: Compare the whole numbers first. 7 > 6. So, 7 $\frac{1}{3}$ > 6 $\frac{2}{3}$

Question 13. 1 $\frac{2}{5}$ _____ 1 $\frac{7}{15}$

Answer: 1 $\frac{2}{5}$ < 1 $\frac{7}{15}$

Explanation: 1 $\frac{2}{5}$ _____ 1 $\frac{7}{15}$ If the whole numbers are the same, compare the fractions. Compare $\frac{2}{5}$ and $\frac{7}{15}$ 5 and 15 are multiples of 15. So, $\frac{2 x 3}{5 x 3}$ = $\frac{6}{15}$ $\frac{6}{15}$ < $\frac{7}{15}$ Use common denominators to write equivalent fractions. 1 $\frac{2}{5}$ < 1 $\frac{7}{15}$

Question 14. Darrell spent 3 $\frac{2}{5}$ hours on a project for school. Jan spent 3 $\frac{1}{4}$ hours and Maeve spent 3.7 hours on the project. Who spent the least amount of time? Show how you found your answer. Then describe another possible method. Type below: __________

Answer: Jan spent the least amount of time.

Explanation: Darrell spent 3 $\frac{2}{5}$ hours on a project for school. Jan spent 3 $\frac{1}{4}$ hours and Maeve spent 3.7 hours on the project. Write the decimal form of 3 $\frac{2}{5}$ = 3.4 Write the decimal form of 3 $\frac{1}{4}$ = 3.25 3.4, 3.25, 3.7 3.25 is the least one. So, Jan spent the least amount of time.

Problem Solving + Applications – Page No. 78

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 5$

Question 15. In one week, Altoona, PA, and Bethlehem, PA, received snowfall every day, Monday through Friday. On which days did Altoona receive over 0.1 inch more snow than Bethlehem? Type below: __________

Answer: Altoona received over 1 inch more snow than Bethlehem on Friday

Explanation: Altoona (converted to decimal form): 2.25, 3.25, 2.625, 4.6, 4.75 Bethlehem: 2.6, 3.2, 2.5, 4.8, 2.7 Altoona received over 1 inch more snow than Bethlehem on Friday

Question 16. What if Altoona received an additional 0.3 inch of snow on Thursday? How would the total amount of snow in Altoona compare to the amount received in Bethlehem that day? Type below: __________

Answer: Altoona received 0.1 inches more snow than Bethlehem on Thursday

Explanation: Altoona received an additional 0.3 inch of snow on Thursday = 4.6 + 0.3 = 4.9 Bethlehem received on Thursday = 4.8 Altoona received 0.1 inches more snow than Bethlehem on Thursday

Question 17. Explain two ways you could compare the snowfall amounts in Altoona and Bethlehem on Monday. Type below: __________

Explanation: Altoona received on Monday = 2.25 Bethlehem received on Monday = 2.6 Bethlehem received 0.35 inches more snow than Altoona on Monday. As the whole numbers are equal compare 1/4 and 0.6. 0.25 < 0.6 So, Altoona received less snow compared to Bethlehem on Monday.

Question 18. Explain how you could compare the snowfall amounts in Altoona on Thursday and Friday. Type below: __________

Answer: Altoona received on Thursday = 4.6 Altoona received on Friday = 4.75 4.6 < 4.75 Altoona received less snow on Thursday compared to Friday.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 6$

Answer: 1/3, 0.39, 2/5, 0.45

Explanation: 1/3 = 0.333 0.45 0.39 2/5 = 0.4 Compare tenths: 3 < 4 Compare hundredths: 0.33 < 0.39 0.4 < 0.45 So, 1/3, 0.39, 2/5, 0.45

Compare and Order Fractions and Decimals – Page No. 79

Write <, >, =.

Question 1. 0.64 _____ $\frac{7}{10}$

Answer: 0.64 < $\frac{7}{10}$

Explanation: Write the decimal form of $\frac{7}{10}$ = 0.7 Compare tenths: 6 < 7 So, 0.64 < 0.7 0.64 < $\frac{7}{10}$

Question 2. 0.48 _____ $\frac{6}{15}$

Answer: 0.48 > $\frac{6}{15}$

Explanation: Write the decimal form of $\frac{6}{15}$ = 0.4 Compare hundredths: 0.48 > 0.4 0.48 > $\frac{6}{15}$

Question 3. 0.75 _____ $\frac{7}{8}$

Answer: 0.75 < $\frac{7}{8}$

Explanation: Write the decimal form of $\frac{7}{8}$ = 0.875 Compare tenths: 7 < 8 0.75 < $\frac{7}{8}$

Question 4. 7 $\frac{1}{8}$ _____ 7.025

Answer: 7 $\frac{1}{8}$ > 7.025

Explanation: Write the decimal form of 7 $\frac{1}{8}$ = 7.125 Compare tenths: 1 > 0 7 $\frac{1}{8}$ > 7.025

Question 5. $\frac{7}{15}$, 0.75, $\frac{5}{6}$ Type below: __________

Answer: $\frac{7}{15}$, 0.75, $\frac{5}{6}$

Explanation: Write the decimal form of $\frac{7}{15}$ = 0.466 0.75 Write the decimal form of $\frac{5}{6}$ = 0.833 Order from least to greatest: $\frac{7}{15}$, 0.75, $\frac{5}{6}$

Question 6. 0.5, 0.41, $\frac{3}{5}$ Type below: __________

Answer: 0.41, 0.5, $\frac{3}{5}$

Explanation: Write the decimal form of $\frac{3}{5}$ = 0.6 Compare tenths: 0.41, 0.5, 0.6 Order from least to greatest: 0.41, 0.5, $\frac{3}{5}$

Question 7. 3.25, 3 $\frac{2}{5}$, 3 $\frac{3}{8}$ Type below: __________

Answer: 3.25, 3 $\frac{2}{5}$, 3 $\frac{3}{8}$

Explanation: Write the decimal form of 3 $\frac{2}{5}$ = 3.4 Write the decimal form of 3 $\frac{3}{8}$ = 3.375 Compare tenths: Order from least to greatest: 3.25, 3 $\frac{2}{5}$, 3 $\frac{3}{8}$

Question 8. 0.9, $\frac{8}{9}$, 0.86 Type below: __________

Answer: 0.86, $\frac{8}{9}$, 0.9

Explanation: Write the decimal form of $\frac{8}{9}$ = 0.88 Compare tenths: 0.86, 0.88, 0.9 Order from least to greatest: 0.86, $\frac{8}{9}$, 0.9

Order from greatest to least.

Question 9. 0.7, $\frac{7}{9}$, $\frac{7}{8}$ Type below: __________

Answer: $\frac{7}{8}$, $\frac{7}{9}$, 0.7

Explanation: 0.7 = 7/10 To compare fractions with the same numerators, compare the denominators. 7/10, 7/9, 7/8 Order from greatest to least: 7/8, 7/9, 7/10

Question 10. 0.2, 0.19, $\frac{3}{5}$ Type below: __________

Answer: $\frac{3}{5}$, 0.2, 0.19

Explanation: Write the decimal form of $\frac{3}{5}$ = 0.6 Compare tenths: 0.6, 0.2, 0.19 Order from greatest to least: $\frac{3}{5}$, 0.2, 0.19

Question 11. 6$\frac{1}{20}$, 6.1, 6.07 Type below: __________

Explanation: Write the decimal form of 6$\frac{1}{20}$ = 121/20 = 6.05 Compare tenths: 6.1, 6.07, 6.05 Order from greatest to least: 6.1, 6.07, 6$\frac{1}{20}$

Question 12. 2 $\frac{1}{2}$, 2.4, 2.35, 2 $\frac{1}{8}$ Type below: __________

Answer: 2 $\frac{1}{2}$, 2.4, 2.35, 2 $\frac{1}{8}$

Explanation: Write the decimal form of 2 $\frac{1}{2}$ = 2.5 Write the decimal form of 2 $\frac{1}{8}$ = 2.125 Compare tenths: 2.5, 2.4, 2.35, 2.125 Order from greatest to least: 2 $\frac{1}{2}$, 2.4, 2.35, 2 $\frac{1}{8}$

Question 13. One day it snowed 3 $\frac{3}{8}$ inches in Altoona and 3.45 inches in Bethlehem. Which city received less snow that day? __________

Answer: Altoona

Explanation: One day it snowed 3 $\frac{3}{8}$ inches in Altoona and 3.45 inches in Bethlehem. Write the decimal form of 3 $\frac{3}{8}$ = 27/8 = 3.375 3.375 < 3.45. Altoona received less snow that day

Question 14. Malia and John each bought 2 pounds of sunflower seeds. Each ate some seeds. Malia has 1 $\frac{1}{3}$ pounds left, and John has 1 $\frac{2}{5}$ pounds left. Who ate more sunflower seeds? __________

Answer: Malia

Explanation: Malia and John each bought 2 pounds of sunflower seeds. Each ate some seeds. Malia has 1 $\frac{1}{3}$ pounds left, and John has 1 $\frac{2}{5}$ pounds left. 2 – 1 $\frac{1}{3}$ = 0.667 2 – 1 $\frac{2}{5}$ = 0.6 0.667 > 0.6 So, Malia ate more sunflower seeds

Question 15. Explain how you would compare the numbers 0.4 and $\frac{3}{8}$. Type below: __________

Answer: Write the decimal form of $\frac{3}{8}$ = 0.375 Compare tenths: 0.4 > 0.375

Lesson Check – Page No. 80

Question 1. Andrea has 3 $\frac{7}{8}$ yards of purple ribbon, 3.7 yards of pink ribbon, and 3 $\frac{4}{5}$ yards of blue ribbon. List the numbers in order from least to greatest. Type below: __________

Answer: Andrea has 3 $\frac{7}{8}$ yards of purple ribbon, 3.7 yards of pink ribbon, and 3 $\frac{4}{5}$ yards of blue ribbon. Write the decimal form of 3 $\frac{7}{8}$ = 3.875 3.7 Write the decimal form of 3 $\frac{4}{5}$ = 3.8 Least to greatest : 3.7, 3 $\frac{4}{5}$, 3 $\frac{7}{8}$

Question 2. Nassim completed $\frac{18}{25}$ of the math homework. Kara completed 0.7 of it. Debbie completed $\frac{5}{8}$ of it. List the numbers in order from greatest to least. Type below: __________

Answer: $1.39, $0.70, $0.63

Explanation: Nassim completed $\frac{18}{25}$ of the math homework. Kara completed 0.7 of it. Debbie completed $\frac{5}{8}$ of it. Write the decimal form of 18/25 = 1.39 0.7 Write the decimal form of 5/8 = 0.63 They are now in order from greatest to least. Think of the amounts as money: $1.39, $0.70, $0.63

Question 3. Tyler bought 3 $\frac{2}{5}$ pounds of oranges. Graph 3 $\frac{2}{5}$ on a number line and write this amount using a decimal. Type below: __________

Question 4. At the factory, a baseball card is placed in every 9th package of cereal. A football card is placed in every 25th package of the cereal. What is the first package that gets both a baseball card and a football card? Type below: __________

Answer: 225th package

Explanation: Look for the first number where both 25 and 9 are a factor of. 25 x 1 = 25 which isn’t a factor of 9, so it won’t be 25. 25 x 2 = 50, which isn’t a factor of 9. 75 is not a factor of 9. (you know because you don’t get a whole number when you divide 75 into 9.) 100 is not a factor of 9, nor is 125, 150, 175, or 200. However, 225 is a factor of both 25 and 9. This makes sense because 25 x 9 is 225. This means that the first package with both will be the 225th package.

Question 5. $15.30 is divided among 15 students. How much does each student receive? $ _____

Answer: $1.02

Explanation: $15.30 is divided among 15 students. $15.30/15 = $1.02 each student receive $1.02

Question 6. Carrie buys 4.16 pounds of apples for $5.20. How much does 1 pound cost? $ _____

Answer: $1.25

Explanation: Carrie buys 4.16 pounds of apples for $5.20. $5.20/4.16 = $1.25 1 pound cost = $1.25

Share and Show – Page No. 83

Find the product. Write it in simplest form.

Question 1. 6 × $\frac{3}{8}$ $\frac{□}{□}$

Answer: $\frac{9}{4}$

Explanation: $\frac{6 × 3}{1 × 8}$ $\frac{18}{8}$ Simplify using the GCF. The GCF of 18 and 8 is 2. Divide the numerator and the denominator by 2. $\frac{18 ÷ 2}{8 ÷ 2}$ = $\frac{9}{4}$

Question 2. $\frac{3}{8}$ × $\frac{8}{9}$ $\frac{□}{□}$

Answer: $\frac{1}{3}$

Explanation: Multiply the numerators and Multiply the denominators. $\frac{3 × 8}{8 × 9}$ = $\frac{24}{72}$ Simplify using the GCF. The GCF of 24 and 72 is 24. Divide the numerator and the denominator by 24. $\frac{24 ÷ 24}{72 ÷ 24}$ = $\frac{1}{3}$

Question 3. Sam and his friends ate 3 $\frac{3}{4}$ bags of fruit snacks. If each bag contained 2 $\frac{1}{2}$ ounces, how many ounces of fruit snacks did Sam and his friends eat? $\frac{□}{□}$

Answer: $\frac{75}{8}$ ounces

Explanation: Sam and his friends ate 3 $\frac{3}{4}$ bags of fruit snacks. If each bag contained 2 $\frac{1}{2}$ ounces 3 $\frac{3}{4}$ x 2 $\frac{1}{2}$ $\frac{15}{4}$ x $\frac{5}{2}$ $\frac{15 x 5}{4 x 2}$ = $\frac{75}{8}$

Attend to Precision Algebra Evaluate using the order of operations.

Write the answer in simplest form.

Question 4. $\left(\frac{3}{4}-\frac{1}{2}\right) \times \frac{3}{5}$ $\frac{□}{□}$

Answer: $\frac{3}{20}$

Explanation: $\left(\frac{3}{4}-\frac{1}{2}\right) \times \frac{3}{5}$ Perform operations in parentheses. $\frac{3}{4}$ – $\frac{1}{2}$ = $\frac{1}{4}$ $\frac{1}{4}$ x $\frac{3}{5}$ = $\frac{1 x 3}{4 x 5}$ = $\frac{3}{20}$

Question 5. $\frac{1}{3}+\frac{4}{9} \times 12$ $\frac{□}{□}$

Answer: $\frac{28}{3}$

Explanation: $\frac{1}{3}$ + $\frac{4}{9}$ = $\frac{7}{9}$ $\frac{7 x 12}{9 x 1}$ = $\frac{84}{9}$ Simplify using the GCF. The GCF of 84 and 9 is 3. Divide the numerator and the denominator by 3. $\frac{84 ÷ 3}{9 ÷ 3}$ = $\frac{28}{3}$

Question 6. $\frac{5}{8} \times \frac{7}{10}-\frac{1}{4}$ $\frac{□}{□}$

Answer: $\frac{11}{16}$

Explanation: $\frac{5 x 7}{8 x 10}$ = $\frac{35}{80}$ $\frac{35}{80}$ – $\frac{1}{4}$ = $\frac{11}{16}$

Question 7. 3 × ($\frac{5}{18}$ + $\frac{1}{6}$) + $\frac{2}{5}$ $\frac{□}{□}$

Answer: $\frac{38}{15}$

Explanation: 3 x $\frac{4}{9}$ + $\frac{2}{5}$ 3 x $\frac{38}{45}$ = $\frac{38}{15}$

Practice: Copy and Solve Find the product. Write it in simplest form.

Question 8. $1 \frac{2}{3} \times 2 \frac{5}{8}$ $\frac{□}{□}$

Answer: $\frac{35}{8}$

Explanation: 1 $\frac{2}{3}$ = $\frac{5}{3}$ 2 $\frac{5}{8}$ = $\frac{21}{8}$ $\frac{5 × 21}{3 × 8}$ = $\frac{105}{24}$ Simplify using the GCF The GCF of 105 and 24 is 3. Divide the numerator and the denominator by 3. $\frac{105 ÷ 3}{24 ÷ 3}$ = $\frac{35}{8}$

Question 9. $\frac{4}{9} \times \frac{4}{5}$ $\frac{□}{□}$

Answer: $\frac{16}{45}$

Explanation: $\frac{4 × 4}{9 × 5}$ = $\frac{16}{45}$

Question 10. $\frac{1}{6} \times \frac{2}{3}$ $\frac{□}{□}$

Answer: $\frac{1}{9}$

Explanation: $\frac{1 × 2}{6 × 3}$ = $\frac{2}{18}$ Simplify using the GCF The GCF of 2 and 18 is 2. Divide the numerator and the denominator by 2. $\frac{2 ÷ 2}{18 ÷ 2}$ = $\frac{1}{9}$

Question 11. $4 \frac{1}{7} \times 3 \frac{1}{9}$ $\frac{□}{□}$

Answer: $\frac{116}{7}$

Explanation: 4$\frac{1}{7}$ = $\frac{29}{7}$ 3$\frac{1}{9}$ = $\frac{28}{9}$ $\frac{29 × 28}{7 × 9}$ = $\frac{812}{63}$ Simplify using the GCF The GCF of 812 and 63 is 7. Divide the numerator and the denominator by 7. $\frac{812 ÷ 7}{63 ÷ 7}$ = $\frac{116}{7}$

Question 12. $\frac{5}{6}$ of the 90 pets in the pet show are cats. $\frac{4}{5}$ of the cats are calico cats. What fraction of the pets are calico cats? How many of the pets are calico cats? Type below: __________

Answer: 60 calico cats

Explanation: 5/6 x 90 = 450/6 = 150/2 150/2 x 4/5 = 60

Question 13. Five cats each ate $\frac{1}{4}$ cup of cat food. Four other cats each ate $\frac{1}{3}$ cup of cat food. How much food did the nine cats eat? Type below: __________

Answer: $\frac{31}{12}$

Explanation: 5 x 1/4 = 5/4 4 x 1/3 = 4/3 5/4 + 4/3 = 31/12

Question 14. $\frac{1}{4} \times\left(\frac{3}{9}+5\right)$ $\frac{□}{□}$

Answer: $\frac{4}{3}$

Explanation: 3/9 + 5 = 16/3 1/4 x 16/3 1 x 16 = 16 4 x 3 = 12 16/12 Simplify using the GCF The GCF of 16 and 12 is 4. Divide the numerator and the denominator by 4. $\frac{16 ÷ 4}{12÷ 4}$ = $\frac{4}{3}$

Question 15. $\frac{9}{10}-\frac{3}{5} \times \frac{1}{2}$ $\frac{□}{□}$

Explanation: 3/5 x 1/2 = 3/10 9/10 – 3/10 = 6/10 Simplify using the GCF The GCF of 6 and 10 is 2. Divide the numerator and the denominator by 2. $\frac{6 ÷ 2}{10 ÷ 2}$ = $\frac{3}{5}$

Question 16. $\frac{4}{5}+\left(\frac{1}{2}-\frac{3}{7}\right) \times 2$ $\frac{□}{□}$

Answer: $\frac{33}{35}$

Explanation: 1/2 – 3/7 = 1/14 1/14 x 2 = 1/7 4/5 + 1/7 = 33/35

Question 17. $15 \times \frac{3}{10}+\frac{7}{8}$ $\frac{□}{□}$

Answer: $\frac{141}{8}$

Explanation: 3/10 + 7/8 = 47/40 15 x 47/40 = 141/8 $\frac{141}{8}$

Page No. 84

Question 18. Write and solve a word problem for the expression $\frac{1}{4} \times \frac{2}{3}$. Show your work. Type below: __________

Answer: $\frac{1}{6}$

Explanation: $\frac{1}{4} \times \frac{2}{3}$ = $\frac{1 X 2}{4 X 3}$ = $\frac{2}{12}$ Simplify using the GCF The GCF of 2 and 12 is 2. Divide the numerator and the denominator by 2. $\frac{2 ÷ 2}{12 ÷ 2}$ = $\frac{1}{6}$

Question 19. Michelle has a recipe that asks for 2 $\frac{1}{2}$ cups of vegetable oil. She wants to use $\frac{2}{3}$ that amount of oil and use applesauce to replace the rest. How much applesauce will she use? Type below: __________

Answer: $\frac{10}{6}$

Explanation: 2 1/2 * 2/3 = 5/2 * 2/3 = 10/6 She will use 10/6 or 1 2/3 cups of vegetable oil

Question 20. Cara’s muffin recipe asks for 1 $\frac{1}{2}$ cups of flour for the muffins and $\frac{1}{4}$ cup of flour for the topping. If she makes $\frac{1}{2}$ of the original recipe, how much flour will she use for the muffins and topping? Type below: __________

Answer: Cara will use 1$\frac{1}{8}$ cups of flour.

Explanation: For first we will find how many cups of flours need to makes the original recipe. Cara uses 1 1/2 cups of flour for the muffins and 1/4 cup off flour for the topping. So, 1 1/2 + 1/4 cups of flour to make the original recipe. 1 1/2 = 3/2 3/2 + 1/4 = 7/4 To make the original recipe Cara needs 7/4 cups of flour. If she makes $\frac{1}{2}$ of the original recipe, then 7/4 x 1/2 = 7/8 = 1 1/8 Cara will use 1 1/8 cups of flour.

Multiply Fractions – Page No. 85

Question 1. $\frac{4}{5} \times \frac{7}{8}$ $\frac{□}{□}$

Answer: $\frac{7}{10}$

Explanation: Multiply the numerators and Multiply the denominators. $\frac{4 × 7}{5 × 8}$ = $\frac{28}{40}$ Simplify using the GCF. The GCF of 28 and 40 is 4. Divide the numerator and the denominator by 4. $\frac{28 ÷ 4}{40 ÷ 4}$ = $\frac{7}{10}$

Question 2. $\frac{1}{8} \times 20$ $\frac{□}{□}$

Answer: $\frac{5}{2}$

Explanation: $\frac{1 × 20}{1 × 8}$ $\frac{20}{8}$ Simplify using the GCF. The GCF of 20 and 8 is 4. Divide the numerator and the denominator by 4. $\frac{20 ÷ 4}{8 ÷ 4}$ = $\frac{5}{2}$

Question 3. $\frac{4}{5} \times \frac{3}{8}$ $\frac{□}{□}$

Answer: $\frac{3}{10}$

Explanation: Multiply the numerators and Multiply the denominators. $\frac{4 × 3}{5 × 8}$ = $\frac{12}{40}$ Simplify using the GCF. The GCF of 12 and 40 is 4. Divide the numerator and the denominator by 4. $\frac{12 ÷ 4}{40 ÷ 4}$ = $\frac{3}{10}$

Question 4. $1 \frac{1}{8} \times \frac{1}{9}$ $\frac{□}{□}$

Answer: $\frac{1}{8}$

Explanation: 1$\frac{1}{8}$ = $\frac{9}{8}$ Multiply the numerators and Multiply the denominators. $\frac{9 × 1}{8 × 9}$ = $\frac{9}{72}$ Simplify using the GCF. The GCF of 9 and 72 is 9. Divide the numerator and the denominator by 9. $\frac{9 ÷ 9}{72 ÷ 9}$ = $\frac{1}{8}$

Question 5. $\frac{3}{4} \times \frac{1}{3} \times \frac{2}{5}$ $\frac{□}{□}$

Answer: $\frac{1}{10}$

Explanation: Multiply the numerators and Multiply the denominators. $\frac{3 × 1 × 2}{4 × 3 × 5}$ = $\frac{6}{60}$ Simplify using the GCF. The GCF of 6 and 60 is 6. Divide the numerator and the denominator by 6. $\frac{6 ÷ 6}{60 ÷ 6}$ = $\frac{1}{10}$

Question 6. Karen raked $\frac{3}{5}$ of the yard. Minni raked $\frac{1}{3}$ of the amount Karen raked. How much of the yard did Minni rake? $\frac{□}{□}$

Explanation: Minni raked 1/5 of the yard. So, minni raked 3/5 of 1/3 means 3/5 x 1/3 Multiply the numerators and Multiply the denominators. $\frac{3 × 1}{5 × 3}$ = $\frac{3}{15}$ Simplify using the GCF. The GCF of 3 and 15 is 3. Divide the numerator and the denominator by 3. $\frac{3 ÷ 3}{15 ÷ 3}$ = $\frac{1}{3}$

Question 7. $\frac{3}{8}$ of the pets in the pet show are dogs. $\frac{2}{3}$ of the dogs have long hair. What fraction of the pets are dogs with long hair? $\frac{□}{□}$

Answer: $\frac{1}{4}$ are dogs with long hair

Explanation: $\frac{3}{8}$ of the pets in the pet show are dogs. $\frac{2}{3}$ of the dogs have long hair. $\frac{3}{8}$ of $\frac{2}{3}$ = $\frac{3 × 2}{8 × 3}$ = $\frac{6}{24}$ The GCF of 6 and 24 is 6. Divide the numerator and the denominator by 6. $\frac{6 ÷ 6}{24 ÷ 6}$ = $\frac{1}{4}$ $\frac{1}{4}$ are dogs with long hair

Evaluate using the order of operations.

Question 8. $\left(\frac{1}{2}+\frac{3}{8}\right) \times 8$ ______

Explanation: 1/2 + 3/8 = 7/8 7/8 × 8 = 7

Question 9. $\frac{3}{4} \times\left(1-\frac{1}{9}\right)$ $\frac{□}{□}$

Answer: $\frac{2}{3}$

Explanation: 1 – 1/9 = 8/9 3/4 × 8/9 = 24/36 The GCF of 24 and 36 is 12. Divide the numerator and the denominator by 12. $\frac{24 ÷ 12}{36 ÷ 12}$ = $\frac{2}{3}$

Question 10. $4 \times \frac{1}{8} \times \frac{3}{10}$ $\frac{□}{□}$

Explanation: Multiply the numerators and Multiply the denominators. $\frac{4 × 1 × 3}{1 × 8 × 10}$ = $\frac{12}{80}$ Simplify using the GCF. The GCF of 12 and 80 is 4. Divide the numerator and the denominator by 4. $\frac{12 ÷ 4}{80 ÷ 4}$ = $\frac{3}{20}$

Question 11. $6 \times\left(\frac{4}{5}+\frac{2}{10}\right) \times \frac{2}{3}$ ______

Explanation: 4/5 + 2/10 = 1 6 × 1 × 2/3 = 12/3 The GCF of 12 and 3 is 4. Divide the numerator and the denominator by 3. $\frac{12 ÷ 3}{3 ÷ 3}$ = $\frac{4}{1}$ = 4

Question 12. Jason ran $\frac{5}{7}$ of the distance around the school track. Sara ran $\frac{4}{5}$ of Jason’s distance. What fraction of the total distance around the track did Sara run? $\frac{□}{□}$

Answer: $\frac{4}{7}$

Explanation: Jason ran $\frac{5}{7}$ of the distance around the school track. Sara ran $\frac{4}{5}$ of Jason’s distance. $\frac{5}{7}$ × $\frac{4}{5}$ = 20/35 The GCF of 20 and 35 is 5. Divide the numerator and the denominator by 5. $\frac{20 ÷ 5}{35 ÷ 5}$ = $\frac{4}{7}$

Question 13. A group of students attend a math club. Half of the students are boys and $\frac{4}{9}$ of the boys have brown eyes. What fraction of the group are boys with brown eyes? $\frac{□}{□}$

Answer: $\frac{2}{9}$ group are boys with brown eyes

Explanation: A group of students attend a math club. Half of the students are boys and $\frac{4}{9}$ of the boys have brown eyes. $\frac{4}{9}$ × $\frac{1}{2}$ = 4/18 = 2/9 2/9 group are boys with brown eyes

Question 14. Write and solve a word problem that involves multiplying by a fraction. Type below: __________

Answer: A group of students attends a math club. Half of the students are boys and $\frac{6}{9}$ of the boys have brown eyes. What fraction of the group are boys with brown eyes? $\frac{□}{□}$ Answer: A group of students attends a math club. Half of the students are boys and $\frac{6}{9}$ of the boys have brown eyes. $\frac{6}{9}$ × $\frac{1}{2}$ = 6/18 = 1/3 1/3 group are boys with brown eyes.

Lesson Check – Page No. 86

Question 1. Veronica’s mom left $\frac{3}{4}$ of a cake on the table. Her brothers ate $\frac{1}{2}$ of it. What fraction of the cake did they eat? $\frac{□}{□}$

Answer: $\frac{2}{4}$

Explanation: Veronica’s mom left $\frac{3}{4}$ of a cake on the table. Her brothers ate $\frac{1}{2}$ of it. Since the fraction of the eaten cake is 1/2, you can multiply the numerator and denominator by and get an equivalent fraction, which is 2/4.

Question 2. One lap around the school track is $\frac{5}{8}$ mile. Carin ran 3 $\frac{1}{2}$ laps. How far did she run? _____ $\frac{□}{□}$

Answer: 2$\frac{3}{16}$

Explanation: One lap around the school track is $\frac{5}{8}$ mile. Carin ran 3 $\frac{1}{2}$ laps. 3 $\frac{1}{2}$ = $\frac{7}{2}$ Therefore, the total distance covered = 7/2 × 5/8 = 35/16 = 2 3/16

Question 3. Tom bought 2 $\frac{5}{16}$ pounds of peanuts and 2.45 pounds of cashews. Which did he buy more of? Explain. Type below: __________

Explanation: Tom bought 2 $\frac{5}{16}$ pounds of peanuts and 2.45 pounds of cashews. 2 $\frac{5}{16}$ = 2.3125 2.3125 < 2.45 He buys more cashews.

Question 4. Eve has 24 stamps each valued at $24.75. What is the total value of her stamps? $ _____

Answer: $594

Explanation: Eve has 24 stamps each valued at $24.75. 24 x $24.75 = $594

Question 5. Naomi went on a 6.5-mile hike. In the morning, she hiked 1.75 miles, rested, and then hiked 2.4 more miles. She completed the hike in the afternoon. How much farther did she hike in the morning than in the afternoon? _____ miles

Answer: Naomi went on a 6.5-mile hike. In the morning, she hiked 1.75 miles, rested, and then hiked 2.4 more miles. She completed the hike in the afternoon. To find how many miles she walked in the afternoon you just subtract the morning miles 4.15 from the total miles 6.5. 6.5 – 4.15 = 2.35 To find how many more miles she walked in the morning you just subtract the morning from the afternoon 4.15 – 2.35=1.8 miles. She hiked 1.8 more miles in the morning

Question 6. A bookstore owner has 48 science fiction books and 30 mysteries he wants to sell quickly. He will make discount packages with one type of book in each. He wants the most books possible in each package, but all packages must contain the same number of books. How many packages can he make? How many packages of each type of book does he have? Type below: __________

Answer: 18 packages

Explanation: The bookstore owner can make 18 possible packages 48 – 30 = 18 packages

Share and Show – Page No. 89

Find the product. Simplify before multiplying.

Question 1. $\frac{5}{6} \times \frac{3}{10}$ $\frac{□}{□}$

Answer: $\frac{1}{4}$

Explanation: $\frac{5}{6} \times \frac{3}{10}$ Multiply the numerators and Multiply the denominators. $\frac{5 × 3}{6 × 10}$ = $\frac{15}{60}$ Simplify using the GCF. The GCF of 15 and 60 is 15. Divide the numerator and the denominator by 15. $\frac{15 ÷ 15}{60 ÷ 15}$ = $\frac{1}{4}$

Question 2. $\frac{3}{4} \times \frac{5}{9}$ $\frac{□}{□}$

Answer: $\frac{5}{12}$

Explanation: $\frac{3}{4} \times \frac{5}{9}$ Multiply the numerators and Multiply the denominators. $\frac{3 × 5}{4 × 9}$ = $\frac{15}{36}$ Simplify using the GCF. The GCF of 15 and 36 is 3. Divide the numerator and the denominator by 3. $\frac{15 ÷ 3}{36 ÷ 3}$ = $\frac{5}{12}$

Question 3. $\frac{2}{3} \times \frac{9}{10}$ $\frac{□}{□}$

Explanation: $\frac{2}{3} \times \frac{9}{10}$ Multiply the numerators and Multiply the denominators. $\frac{2 × 9}{3 × 10}$ = $\frac{18}{30}$ Simplify using the GCF. The GCF of 18 and 30 is 6. Divide the numerator and the denominator by 6. $\frac{18 ÷ 6}{30 ÷ 6}$ = $\frac{3}{5}$

Question 4. After a picnic, $\frac{5}{12}$ of the cornbread is left over. Val eats $\frac{3}{5}$ of the leftover cornbread. What fraction of the cornbread does Val eat? $\frac{□}{□}$

Explanation: After a picnic, $\frac{5}{12}$ of the cornbread is left over. Val eats $\frac{3}{5}$ of the leftover cornbread. $\frac{5}{12} \times \frac{3}{5}$ Multiply the numerators and Multiply the denominators. $\frac{5 × 3}{12 × 5}$ = $\frac{15}{60}$ Simplify using the GCF. The GCF of 15 and 60 is 15. Divide the numerator and the denominator by 15. $\frac{15 ÷ 15}{60 ÷ 15}$ = $\frac{1}{4}$

Question 5. The reptile house at the zoo has an iguana that is $\frac{5}{6}$ yd long. It has a Gila monster that is $\frac{4}{5}$ of the length of the iguana. How long is the Gila monster? $\frac{□}{□}$

Explanation: The reptile house at the zoo has an iguana that is $\frac{5}{6}$ yd long. It has a Gila monster that is $\frac{4}{5}$ of the length of the iguana. $\frac{5}{6} \times \frac{4}{5}$ Multiply the numerators and Multiply the denominators. $\frac{5 × 4}{6× 5}$ = $\frac{20}{30}$ Simplify using the GCF. The GCF of 20 and 30 is 10. Divide the numerator and the denominator by 10. $\frac{20 ÷ 10}{30 ÷ 10}$ = $\frac{2}{3}$

Question 6. $\frac{3}{4} \times \frac{1}{6}$ $\frac{□}{□}$

Explanation: $\frac{3}{4} \times \frac{1}{6}$ Multiply the numerators and Multiply the denominators. $\frac{3 × 1}{4 × 6}$ = $\frac{3}{24}$ Simplify using the GCF. The GCF of 3 and 24 is 3. Divide the numerator and the denominator by 3. $\frac{3 ÷ 3}{24 ÷ 3}$ = $\frac{1}{8}$

Question 7. $\frac{7}{10} \times \frac{2}{3}$ $\frac{□}{□}$

Answer: $\frac{7}{15}$

Explanation: $\frac{7}{10} \times \frac{2}{3}$ Multiply the numerators and Multiply the denominators. $\frac{7 × 2}{10 × 3}$ = $\frac{14}{30}$ Simplify using the GCF. The GCF of 14 and 30 is 2. Divide the numerator and the denominator by 2. $\frac{14 ÷ 2}{30 ÷ 2}$ = $\frac{7}{15}$

Question 8. $\frac{5}{8} \times \frac{2}{5}$ $\frac{□}{□}$

Explanation: $\frac{5}{8} \times \frac{2}{5}$ Multiply the numerators and Multiply the denominators. $\frac{5 × 2}{8 × 5}$ = $\frac{10}{40}$ Simplify using the GCF. The GCF of 10 and 40 is 10. Divide the numerator and the denominator by 10. $\frac{10 ÷ 10}{40 ÷ 10}$ = $\frac{1}{4}$

Question 9. $\frac{9}{10} \times \frac{5}{6}$ $\frac{□}{□}$

Answer: $\frac{3}{4}$

Explanation: $\frac{9}{10} \times \frac{5}{6}$ Multiply the numerators and Multiply the denominators. $\frac{9 × 5}{10 × 6}$ = $\frac{45}{60}$ Simplify using the GCF. The GCF of 45 and 60 is 15. Divide the numerator and the denominator by 15. $\frac{45 ÷ 15}{60 ÷ 15}$ = $\frac{3}{4}$

Question 10. $\frac{11}{12} \times \frac{3}{7}$ $\frac{□}{□}$

Answer: $\frac{11}{28}$

Explanation: $\frac{11}{12} \times \frac{3}{7}$ Multiply the numerators and Multiply the denominators. $\frac{11 × 3}{12 × 7}$ = $\frac{33}{84}$ Simplify using the GCF. The GCF of 33 and 84 is 3. Divide the numerator and the denominator by 3. $\frac{33 ÷ 3}{84 ÷ 3}$ = $\frac{11}{28}$

Question 11. Shelley’s basketball team won $\frac{3}{4}$ of their games last season. In $\frac{1}{6}$ of the games they won, they outscored their opponents by more than 10 points. What fraction of their games did Shelley’s team win by more than 10 points? $\frac{□}{□}$

Explanation: Let the total number of games be x. Number of games Shelley’s team won = 3/4x Number of games they outscored their opponents by more than 10 points = 1/6 X 3/4x = 1/8x Hence, 1/8 of the total games, Shelley’s team won by 10 points.

Question 12. Mr. Ortiz has $\frac{3}{4}$ pound of oatmeal. He uses $\frac{2}{3}$ of the oatmeal to bake muffins. How much oatmeal does Mr. Ortiz have left? $\frac{□}{□}$

Explanation: Mr. Ortiz has $\frac{3}{4}$ pound of oatmeal. He uses $\frac{2}{3}$ of the oatmeal to bake muffins. $\frac{3}{4} \times \frac{2}{3}$ Multiply the numerators and Multiply the denominators. $\frac{3 × 2}{4 × 3}$ = $\frac{6}{12}$ Simplify using the GCF. The GCF of 6 and 12 is 6. Divide the numerator and the denominator by 6. $\frac{6 ÷ 6}{12 ÷ 6}$ = $\frac{1}{2}$

Question 13. Compare Strategies To find $\frac{16}{27}$ × $\frac{3}{4}$, you can multiply the fractions and then simplify the product or you can simplify the fractions and then multiply. Which method do you prefer? Explain. Type below: __________

Answer: $\frac{16}{27}$ × $\frac{3}{4}$ $\frac{16 × 3}{27 × 4}$ = $\frac{16 × 3}{4 × 27}$ $\frac{48}{96}$ Simplify using the GCF. The GCF of 48 and 96 is 48. Divide the numerator and the denominator by 48. $\frac{48 ÷ 48}{96 ÷ 48}$ = $\frac{1}{2}$

Problem Solving + Applications – Page No. 90

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 7$

Question 14. Three students each popped $\frac{3}{4}$ cup of popcorn kernels. The table shows the fraction of each student’s kernels that did not pop. Which student had $\frac{1}{16}$ cup unpopped kernels? __________

Answer: Mirza

Explanation: Three students each popped $\frac{3}{4}$ cup of popcorn kernels. The table shows the fraction of each student’s kernels that did not pop. Katie = 3/4 x 1/10 = 3/40 Mirza = 3/4 x 1/12 = 1/16

Question 15. The jogging track at Francine’s school is $\frac{3}{4}$ mile long. Yesterday Francine completed two laps on the track. If she ran $\frac{1}{3}$ of the distance and walked the remainder of the way, how far did she walk? ____ mile

Answer: 1 mile

Explanation: Length of jogging track at Francine’s school = 3/4 mile Let the distance covered by running be = x Let the distance covered by walking be = y Total number of laps completed by Francine = 2 Total distance covered by Francine = number of laps X distance covered in one lap 2 x 3/4 = 3/25 mile Now, distance covered by running = 1/3 of the total distance x = 1/3 x 3/2 distance covered by walking y = total distance – distance covered by running 3/2 – x = 3/2 – 1/2 = 1 mile Hence, Francine walked for 1 mile.

Question 16. At a snack store, $\frac{7}{12}$ of the customers bought pretzels and $\frac{3}{10}$ of those customers bought low-salt pretzels. Bill states that $\frac{7}{30}$ of the customers bought low-salt pretzels. Does Bill’s statement make sense? Explain. Type below: __________

Answer: Bill’s statement does not make sense because it is incorrect: 7/12 customers bought pretzels. 3/10 Of those customers bought low salt pretzels (x) 3/10 of 7/12 = x 21/120 = x Simplify: 7/40 To be correct, Bill would have to say that 7/40 of the customers bought low salt pretzels, but instead, he had said 7/30.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 8$

Simplify Factors – Page No. 91

Question 1. $\frac{8}{9} \times \frac{5}{12}$ $\frac{□}{□}$

Answer: $\frac{10}{27}$

Explanation: $\frac{8}{9} \times \frac{5}{12}$ Multiply the numerators and Multiply the denominators. $\frac{8 × 5}{9 × 12}$ = $\frac{40}{108}$ Simplify using the GCF. The GCF of 40 and 108 is 4. Divide the numerator and the denominator by 4. $\frac{40 ÷ 4}{108 ÷ 4}$ = $\frac{10}{27}$

Question 2. $\frac{3}{4} \times \frac{16}{21}$ $\frac{□}{□}$

Explanation: $\frac{3}{4} \times \frac{16}{21}$ Multiply the numerators and Multiply the denominators. $\frac{3 × 16}{4 × 21}$ = $\frac{48}{84}$ Simplify using the GCF. The GCF of 48 and 84 is 12. Divide the numerator and the denominator by 12. $\frac{48 ÷ 12}{84 ÷ 12}$ = $\frac{4}{7}$

Question 3. $\frac{15}{20} \times \frac{2}{5}$ $\frac{□}{□}$

Explanation: $\frac{15}{20} \times \frac{2}{5}$ Multiply the numerators and Multiply the denominators. $\frac{15 × 2}{20 × 5}$ = $\frac{30}{100}$ Simplify using the GCF. The GCF of 30 and 100 is 10. Divide the numerator and the denominator by 10. $\frac{30 ÷ 10}{100 ÷ 10}$ = $\frac{3}{10}$

Question 4. $\frac{9}{18} \times \frac{2}{3}$ $\frac{□}{□}$

Explanation: $\frac{9}{18} \times \frac{2}{3}$ Multiply the numerators and Multiply the denominators. $\frac{9 × 2}{18 × 3}$ = $\frac{18}{54}$ Simplify using the GCF. The GCF of 18 and 54 is 18. Divide the numerator and the denominator by 18. $\frac{18 ÷ 18}{54 ÷ 18}$ = $\frac{1}{3}$

Question 5. $\frac{3}{4} \times \frac{7}{30}$ $\frac{□}{□}$

Answer: $\frac{7}{40}$

Explanation: $\frac{3}{4} \times \frac{7}{30}$ Multiply the numerators and Multiply the denominators. $\frac{3 × 7}{4 × 30}$ = $\frac{21}{120}$ Simplify using the GCF. The GCF of 21 and 120 is 3. Divide the numerator and the denominator by 3. $\frac{21 ÷ 3}{120 ÷ 3}$ = $\frac{7}{40}$

Question 6. $\frac{8}{15} \times \frac{15}{32}$ $\frac{□}{□}$

Explanation: $\frac{8}{15} \times \frac{15}{32}$ Multiply the numerators and Multiply the denominators. $\frac{8 × 15}{15 × 32}$ = $\frac{120}{480}$ Simplify using the GCF. The GCF of 120 and 480 is 120. Divide the numerator and the denominator by 120. $\frac{120 ÷ 120}{480 ÷ 120}$ = $\frac{1}{4}$

Question 7. $\frac{12}{21} \times \frac{7}{9}$ $\frac{□}{□}$

Answer: $\frac{4}{9}$

Explanation: $\frac{12}{21} \times \frac{7}{9}$ Multiply the numerators and Multiply the denominators. $\frac{12 × 7}{21 × 9}$ = $\frac{84}{189}$ Simplify using the GCF. The GCF of 84 and 189 is 21. Divide the numerator and the denominator by 21. $\frac{84 ÷ 21}{189 ÷ 21}$ = $\frac{4}{9}$

Question 8. $\frac{18}{22} \times \frac{8}{9}$ $\frac{□}{□}$

Answer: $\frac{8}{11}$

Explanation: $\frac{18}{22} \times \frac{8}{9}$ Multiply the numerators and Multiply the denominators. $\frac{18 × 8}{22 × 9}$ = $\frac{144}{198}$ Simplify using the GCF. The GCF of 144 and 198 is 18. Divide the numerator and the denominator by 18. $\frac{144 ÷ 18}{198 ÷ 18}$ = $\frac{8}{11}$

Question 9. Amber has a $\frac{4}{5}$-pound bag of colored sand. She uses $\frac{1}{2}$ of the bag for an art project. How much sand does she use for the project? $\frac{□}{□}$ pounds

Answer: $\frac{2}{5}$ pounds

Explanation: Amber has a $\frac{4}{5}$-pound bag of colored sand. She uses $\frac{1}{2}$ of the bag for an art project. 4/5 X 1/2 = 2/5

Question 10. Tyler has $\frac{3}{4}$ month to write a book report. He finished the report in $\frac{2}{3}$ that time. How much time did it take Tyler to write the report? $\frac{□}{□}$ month

Answer: $\frac{1}{2}$ month

Explanation: Tyler has $\frac{3}{4}$ month to write a book report. He finished the report in $\frac{2}{3}$ that time. 3/4 X 2/3 = 1/2

Question 11. Show two ways to multiply $\frac{2}{15} \times \frac{3}{20}$. Then tell which way is easier and justify your choice. Type below: __________

Answer: $\frac{2}{15} \times \frac{3}{20}$ 2/15 X 3/20 = 2/20 X 3/15 = 1/10 X 1/5 = 1/50

Lesson Check – Page No. 92

Find each product. Simplify before multiplying.

Question 1. At Susie’s school, $\frac{5}{8}$ of all students play sports. Of the students who play sports, $\frac{2}{5}$ play soccer. What fraction of the students in Susie’s school play soccer? $\frac{□}{□}$

Explanation: At Susie’s school, $\frac{5}{8}$ of all students play sports. Of the students who play sports, $\frac{2}{5}$ play soccer. Multiply 5/8 X 2/5, and the answer is 0.25, which converts to 25/100 or 1/4

Question 2. A box of popcorn weighs $\frac{15}{16}$ pounds. The box contains $\frac{1}{3}$ buttered popcorn and $\frac{2}{3}$ cheesy popcorn. How much does the cheesy popcorn weigh? $\frac{□}{□}$

Answer: $\frac{5}{8}$

Explanation: Total weight of a box of popcorn =15/16 pounds. We are given two types of popcorns are there, butter popcorns and cheesy popcorns. Butter popcorn is the one-third of the total weight = 1/3 of the Total weight Plugging the value of the total weight, we get = 1/3 * 15/16 = 5/16 pounds. Cheesy popcorn = 2/3 of Total weight Plugging the value of total weight, we get = 2/3 * 15/16 = 10/16 or 5/8 pounds. Therefore, cheesy popcorn weighs is 5/8 pounds.

Question 3. Ramòn bought a dozen ears of corn for $1.80. What was the cost of each ear of corn? $ ______

Answer: $0.15

Explanation: Ramòn bought a dozen ears of corn for $1.80. So, for the cost of each ear of corn, $1.80/12 = $0.15

Question 4. A 1.8-ounce jar of cinnamon costs $4.05. What is the cost per ounce? $ ______

Answer: $2.25 per ounce

Explanation: If a 1.8-ounce jar costs $4.05, do $4.05 divided by 1.8. $4.05 / 1.8 = $2.25 per ounce.

Question 5. Rose bought $\frac{7}{20}$ kilogram of ginger candy and 0.4 kilogram of cinnamon candy. Which did she buy more of? Explain how you know. Type below: __________

Answer: Rose bought ginger candy = 7/20 kilogram = 0.35 Kilogram She bought cinnamon candy = 0.4 kilogram 0.4 > 0.35 Therefore, She bought cinnamon candy more.

Question 6. Don walked 3 $\frac{3}{5}$ miles on Friday, 3.7 miles on Saturday, and 3 $\frac{5}{8}$ miles on Sunday. List the distances from least to greatest. Type below: __________

Answer: 3 $\frac{3}{5}$, 3 $\frac{5}{8}$, 3.7

Explanation: 3 $\frac{3}{5}$ = 18/5 = 3.6 3 $\frac{5}{8}$ = 29/8 = 3.625 3.6 < 3.625 < 3.7 3 $\frac{3}{5}$, 3 $\frac{5}{8}$, 3.7

Mid-Chapter Checkpoint – Vocabulary – Page No. 93

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 9$

Question 1. The fractions $\frac{1}{2}$ and $\frac{5}{10}$ are _____. Type below: __________

Answer: Equivalent fractions

Question 2. A _____ is a denominator that is the same in two or more fractions. Type below: __________

Answer: Common Denominator

Concepts and Skills

Write as a decimal. Tell whether you used division, a number line, or some other method.

Question 3. $\frac{7}{20}$ _____

Answer: 0.35

Explanation: By using Division, $\frac{7}{20}$ = 0.35

Question 4. 8 $\frac{39}{40}$ _____

Answer: 8.975

Explanation: By using Division, 8 $\frac{39}{40}$ = 359/40 = 8.975

Question 5. 1 $\frac{5}{8}$ _____

Answer: 1.625

Explanation: By using Division, 1 $\frac{5}{8}$ = 13/8 = 1.625

Question 6. $\frac{19}{25}$ _____

Answer: 0.76

Explanation: By using Division, $\frac{19}{25}$ = 0.76

Question 7. $\frac{4}{5}, \frac{3}{4}, 0.88$ Type below: __________

Answer: $\frac{3}{4}$, $\frac{4}{5}$,0.88

Explanation: Write the decimal form of 4/5 = 0.8 Write the decimal form of 3/4 = 0.75 0.88 0.75 < 0.8 < 0.88

Question 8. 0.65, 0.59, $\frac{3}{5}$ Type below: __________

Answer: 0.59, $\frac{3}{5}$, 0.65

Explanation: Write the decimal form of 3/5 = 0.6 0.59 < 0.6 < 0.65

Question 9. $1 \frac{1}{4}, 1 \frac{2}{3}, \frac{11}{12}$ Type below: __________

Answer: $\frac{11}{12}$, 1$\frac{1}{4}$, 1$\frac{2}{3}$

Explanation: Write the decimal form of 1 1/4 = 5/4 = 1.25 Write the decimal form of 1 2/3 = 5/3 = 1.66 Write the decimal form of 11/12 = 0.916 0.916 < 1.25 < 1.66

Question 10. 0.9, $\frac{7}{8}$, 0.86 Type below: __________

Answer: 0.86, $\frac{7}{8}$, 0.9

Explanation: Write the decimal form of $\frac{7}{8}$ = 0.875 0.86 < 0.875 < 0.9

Question 11. $\frac{2}{3} \times \frac{1}{8}$ $\frac{□}{□}$

Answer: $\frac{1}{12}$

Explanation: $\frac{2}{3} \times \frac{1}{8}$ Multiply the numerators and Multiply the denominators. $\frac{2 × 1}{3 × 8}$ = $\frac{2}{24}$ Simplify using the GCF. The GCF of 2 and 24 is 2. Divide the numerator and the denominator by 2. $\frac{2 ÷ 2}{24 ÷ 2}$ = $\frac{1}{12}$

Question 12. $\frac{4}{5} \times \frac{2}{5}$ $\frac{□}{□}$

Answer: $\frac{8}{25}$

Explanation: $\frac{4}{5} \times \frac{2}{5}$ Multiply the numerators and Multiply the denominators. $\frac{4 × 2}{5 × 5}$ = $\frac{8}{25}$

Question 13. 12 × $\frac{3}{4}$ _____

Explanation: 12 × $\frac{3}{4}$ Multiply the numerators and Multiply the denominators. $\frac{12 × 3}{1 × 4}$ = $\frac{36}{4}$ = 9

Question 14. Mia climbs $\frac{5}{8}$ of the height of the rock wall. Lee climbs $\frac{4}{5}$ of Mia’s distance. What fraction of the wall does Lee climb? $\frac{□}{□}$

Explanation: find the LCM (least common denominator) for 5/8 and 4/5. 5/8= 25/40 and 4/5= 32/40. Subtract and you get 7/40.

Page No. 94

Question 15. In Zoe’s class, $\frac{4}{5}$ of the students have pets. Of the students who have pets, $\frac{1}{8}$ have rodents. What fraction of the students in Zoe’s class have pets that are rodents? What fraction of the students in Zoe’s class have pets that are not rodents? Type below: __________

Answer: $\frac{1}{10}$ of the students in Zoe’s class have pets that are rodents $\frac{7}{10}$ of the students in Zoe’s class have pets that are not rodents

Explanation: In Zoe’s class, $\frac{4}{5}$ of the students have pets. Of the students who have pets, $\frac{1}{8}$ have rodents. 4/5 X 1/8 = 1/10 4/5 – 1/10 = 7/10

Question 16. A recipe calls for 2 $\frac{2}{3}$ cups of flour. Terell wants to make $\frac{3}{4}$ of the recipe. How much flour should he use? _____ cups

Answer: 2 cups

Explanation: 2 $\frac{2}{3}$ = 8/3 8/3 * 3/4 = 2

Question 17. Following the Baltimore Running Festival in 2009, volunteers collected and recycled 3.75 tons of trash. Graph 3.75 on a number line and write the weight as a mixed number. Type below: __________

Answer: Volunteers collected and recycled 3.75 tons of trash. We need to convert 3.75 as a mixed number. The mixed number consists of a whole number and a proper fraction. In the given number 3.75, 3 as the whole number and convert 0.75 to a fraction. 3.75 = 3 + 0.75 = 3 + 75/100 We can reduce the fraction 75/ 100 = 3+ 3/4 = 3 3/4

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 10$

Answer: 22/25 = 0.88 17/20 = 0.85 4/5 = 0.8 3/4 = 0.75 Monica had the highest score Let x be the total number of points: (22/25 + 17/20 + 4/5 + 3/4)x = 80 x = 24.39 That is not a whole number of points.

Share and Show – Page No. 97

Use the model to find the quotient.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 11$

Explanation: 1/2 groups of 3 $\frac{1}{2}$ ÷ 3 1/2 × 1/3 = 1/6

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 12$

Explanation: 3/4 groups of 3/8 3/4 × 8/3 = 2

Use fraction strips to find the quotient. Then draw the model.

Question 3. $\frac{1}{3}$ ÷ 4 $\frac{□}{□}$

Explanation: $\frac{1}{3}$ ÷ 4 $\frac{1}{3}$ × $\frac{1}{4}$ $\frac{1}{12}$

Question 4. $\frac{3}{5} \div \frac{3}{10}$ ______

Explanation: $\frac{3}{5} \div \frac{3}{10}$ $\frac{3}{5}$ × $\frac{10}{3}$ 2

Draw a model to solve. Then write an equation for the model. Interpret the result.

Question 5. How many $\frac{1}{4}$ cup servings of raisins are in $\frac{3}{8}$ cup of raisins? Type below: __________

Answer: 1.5

Explanation: 3/8 × 1/4 = 1.5

Question 6. How many $\frac{1}{3}$ lb bags of trail mix can Josh make from $\frac{5}{6}$ lb of trail mix? Type below: __________

Explanation: Multiply 1/3 with 2 1/3 × 2 = 2/6. 2/6 can go into 5/6 twice so the answer is two bags.

Question 7. Pose a Problem Write and solve a problem for $\frac{3}{4}$ ÷ 3 that represents how much in each of 3 groups. Type below: __________

Explanation: $\frac{3}{4}$ ÷ 3 $\frac{3}{4}$ × $\frac{1}{3}$ = 1/4

Problem Solving + Applications – Page No. 98

The table shows the amount of each material that students in a sewing class need for one purse.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 13$

Question 8. Mrs. Brown has $\frac{1}{3}$ yd of blue denim and $\frac{1}{2}$ yd of black denim. How many purses can be made using denim as the main fabric? _____ purses

Answer: 5 purses

Explanation: Mrs. Brown has $\frac{1}{3}$ yd of blue denim and $\frac{1}{2}$ yd of black denim. 3 + 2 = 5

Question 9. One student brings $\frac{1}{2}$ yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbon will each student receive? Will each of them have enough ribbon for a purse? Explain. Type below: __________

Answer: One student brings $\frac{1}{2}$ yd of ribbon. If 3 students receive an equal length of the ribbon, $\frac{1}{2}$ ÷ 3 1/2 × 1/3 = 1/6 They don’t have enough ribbon for a purse

Question 10. Make Arguments There was $\frac{1}{2}$ yd of purple and pink striped fabric. Jessie said she could only make $\frac{1}{24}$ of a purse using that fabric as the trim. Is she correct? Use what you know about the meanings of multiplication and division to defend your answer. Type below: __________

Answer: There was $\frac{1}{2}$ yd of purple and pink striped fabric. Jessie said she could only make $\frac{1}{24}$ of a purse using that fabric as the trim. 1/2 × 12 = 1/24 So, 12 is the answer

Question 11. Draw a model to find the quotient. $\frac{1}{2}$ ÷ 4 = Type below: __________

Explanation: 1/2 × 1/4 = 1/8

Model Fraction Division – Page No. 99

Use the model to find the quotient

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 14$

Explanation: $\frac{1}{4}$ ÷ 3 $\frac{1}{4}$ × $\frac{1}{3}$ = $\frac{1}{12}$

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 15$

Explanation: $\frac{1}{2} \div \frac{2}{12}=$ $\frac{1}{2}$ × $\frac{12}{2}$ = $\frac{12}{4}$ = 3

Use fraction strips to find the quotient.

Question 3. $\frac{5}{6} \div \frac{1}{2}=$ ______ $\frac{□}{□}$

Answer: $\frac{5}{3}$

Explanation: $\frac{5}{6} \div \frac{1}{2}=$ $\frac{5}{6}$ × $\frac{2}{1}$ = $\frac{5}{3}$

Question 4. $\frac{2}{3}$ ÷ 4 = $\frac{□}{□}$

Explanation: $\frac{2}{3}$ ÷ 4 $\frac{2}{3}$ × $\frac{1}{4}$ = $\frac{2}{12}$ = 1/6

Question 5. $\frac{1}{2}$ ÷ 6 = $\frac{□}{□}$

Explanation: $\frac{1}{2}$ ÷ 6 $\frac{1}{2}$ × $\frac{1}{6}$ = $\frac{1}{12}$

Question 6. $\frac{1}{3} \div \frac{1}{12}$ ______

Explanation: $\frac{1}{3} \div \frac{1}{12}$ $\frac{1}{3}$ × $\frac{12}{1}$ = $\frac{12}{3}$ = 4

Question 7. If Jerry runs $\frac{1}{10}$ mile each day, how many days will it take for him to run $\frac{4}{5}$ mile? ______ days

Answer: 8 days

Explanation: If Jerry runs $\frac{1}{10}$ mile each day, $\frac{4}{5}$ ÷ $\frac{1}{10}$ $\frac{4}{5}$ × $\frac{10}{1}$ = $\frac{40}{5}$ = 8

Question 8. Mrs. Jennings has $\frac{3}{4}$ gallon of paint for an art project. She plans to divide the paint equally into jars. If she puts $\frac{1}{8}$ gallon of paint into each jar, how many jars will she use? ______ jars

Answer: 6 jars

Explanation: Mrs. Jennings has 3/4 Gallons of paint for an art project. In 1 jar she puts 1/8 gallon of paint. The number of jars in which she plans to to divide the paint equally is given by, n= 3/4 ÷ 1/8 n = $\frac{3}{4}$ × $\frac{8}{1}$ = $\frac{24}{4}$ = 6

Question 9. If one jar of glue weighs $\frac{1}{12}$ pound, how many jars can Rickie get from $\frac{2}{3}$ pound of glue? ______ jars

Answer: 8 jars

Explanation: The weight of glue in one jar = 1/12 pound To get 2/3 pound of glue Rickie can get the number of jars 2/3 ÷ 1/12 2/3 × 12/1 = 24/3 = 8

Question 10. Explain how to use a model to show $\frac{2}{6} \div \frac{1}{12}$ and $\frac{2}{6}$ ÷ 4. Type below: __________

Explanation: $\frac{2}{6} \div \frac{1}{12}$ 2/6 = 1/3 1/3 x 12/1 = 4 $\frac{2}{6}$ ÷ 4 1/3 x 1/4 = 1/12

Lesson Check – Page No. 100

Question 1. Darcy needs $\frac{1}{4}$ yard of fabric to make a banner. She has 2 yards of fabric. How many banners can she make? ______ banners

Answer: 8 banners

Explanation: Darcy needs $\frac{1}{4}$ yard of fabric to make a banner. She has 2 yards of fabric. 2 ÷ $\frac{1}{4}$ = 2 x 4 = 8

Question 2. Lorenzo bought $\frac{15}{16}$ pounds of ground beef. He wants to make hamburgers that weigh $\frac{3}{16}$ pound each. How many hamburgers can he make? ______ hamburgers

Answer: 5 hamburgers

Explanation: Lorenzo bought $\frac{15}{16}$ pounds of ground beef. He wants to make hamburgers that weigh $\frac{3}{16}$ pound each. $\frac{15}{16}$ ÷ $\frac{3}{16}$ 15/3 = 5

Question 3. Letisha wants to read 22 pages a night. At that rate, how long will it take her to read a book with 300 pages? ______ nights

Answer: 14 nights

Explanation: Letisha wants to read 22 pages a night. It takes her to read a book with 300 pages 300/22 = 13.6 13.6 is near to 14 So, it is for 2 weeks.

Question 4. A principal wants to order enough notebooks for 624 students. The notebooks come in boxes of 28. How many boxes should he order? ______ boxes

Answer: 22 boxes

Explanation: A principal wants to order enough notebooks for 624 students. The notebooks come in boxes of 28. 624/28 = 22.2857 22.2857 is closer to 22 22 boxes.

Question 5. Each block in Ton’s neighborhood is $\frac{2}{3}$ mile long. If he walks 4 $\frac{1}{2}$ blocks, how far does he walk? ______ miles

Answer: 3 miles

Explanation: If each block is 2/3 miles long, and he walks 4 1/2 blocks, we can simply multiply to two. It looks like this: (2/3)(4 1/2) to multiply, make 4 1/2 into an improper fraction and multiply normally (2/3)(9/4) Ton walks 3 miles total.

Question 6. In Cathy’s garden, $\frac{5}{6}$ of the area is planted with flowers. Of the flowers, $\frac{3}{10}$ of them are red. What fraction of Cathy’s garden is planted with red flowers? $\frac{□}{□}$

Explanation: In Cathy’s garden, $\frac{5}{6}$ of the area is planted with flowers. Of the flowers, $\frac{3}{10}$ of them are red. 5/6 x 3/10 = 1/4

Share and Show – Page No. 103

Estimate using compatible numbers.

Question 1. $22 \frac{4}{5} \div 6 \frac{1}{4}$ _______

Explanation: 22 $\frac{4}{5}$ = 114/5 = 22.8 6 $\frac{1}{4}$ = 25/4 = 6.25 22.8 is closer to 24 6.25 is closer to 6 24/6 = 4

Question 2. $12 \div 3 \frac{3}{4}$ _______

Explanation: 3 $\frac{3}{4}$ = 15/4 = 3.75 3.75 is closer to 4 12/4 = 3

Question 3. $33 \frac{7}{8} \div 5 \frac{1}{3}$ _______

Explanation: 33 $\frac{7}{8}$ = 271/8 = 33.875 5 $\frac{1}{3}$ = 16/3 = 5.333 33.875 is closer to 35 5.333 is closer to 5 35/5 = 7

Question 4. $3 \frac{7}{8} \div \frac{5}{9}$ _______

Explanation: 3 $\frac{7}{8}$ = 31/8 = 3.875 $\frac{5}{9}$ = 0.555 3.875 is closer to 4 0.555 is closer to 1 4/1 = 4

Question 5. $34 \frac{7}{12} \div 7 \frac{3}{8}$ _______

Explanation: 34 $\frac{7}{12}$ = 415/12 = 34.583 7 $\frac{3}{8}$ = 59/8 = 7.375 34.583 is closer to 35 7.375 is closer to 7 35/7 = 5

Question 6. $1 \frac{2}{9} \div \frac{1}{6}$ _______

Explanation: 1 $\frac{2}{9}$ = 11/9 = 1.222 $\frac{1}{6}$ = 0.1666 1.222 is closer to 1 0.1666 is closer to 0.2 1/0.2 = 5

Question 7. $44 \frac{1}{4} \div 11 \frac{7}{9}$ _______

Explanation: 44 $\frac{1}{4}$ = 177/4 = 44.25 11 $\frac{7}{9}$ = 106/9 = 11.77 44.25 is closer to 44 11.77 is closer to 11 44/11 = 4

Question 8. $71 \frac{11}{12} \div 8 \frac{3}{4}$ _______

Explanation: 71 $\frac{11}{12}$ = 863/12 = 71.916 8 $\frac{3}{4}$ = 35/4 = 8.75 71.916 is closer to 72 8.75 is closer to 9 72/9 = 8

Question 9. $1 \frac{1}{6} \div \frac{1}{8}$ _______

Explanation: 1 $\frac{1}{6}$ = 7/6 = 1.166 $\frac{1}{8}$ = 0.125 1.166 is closer to 1.2 0.125 is closer to 0.1 1.2/0.1 = 12

Estimate to compare. Write <, >, or =.

Question 10. $21 \frac{3}{10} \div 2 \frac{5}{6}$ _______ $35 \frac{7}{9} \div 3 \frac{2}{3}$

Answer: $21 \frac{3}{10} \div 2 \frac{5}{6}$ < $35 \frac{7}{9} \div 3 \frac{2}{3}$

Explanation: 21 $\frac{3}{10}$ = 213/10 = 21.3 2 $\frac{5}{6}$ = 17/6 = 2.833 21.3 is closer to 21 2.833 is closer to 3 21/3 = 7 35 $\frac{7}{9}$ = 322/9 = 35.777 3 $\frac{2}{3}$ = 11/3 = 3.666 35.777 is closer to 36 3.666 is closer to 4 36/4 = 9 7 < 9 So, $21 \frac{3}{10} \div 2 \frac{5}{6}$ < $35 \frac{7}{9} \div 3 \frac{2}{3}$

Question 11. $29 \frac{4}{5} \div 5 \frac{1}{6}$ _______ $27 \frac{8}{9} \div 6 \frac{5}{8}$

Answer: $29 \frac{4}{5} \div 5 \frac{1}{6}$ > $27 \frac{8}{9} \div 6 \frac{5}{8}$

Explanation: 29 $\frac{4}{5}$ = 149/5 = 29.8 5 $\frac{1}{6}$ = 31/6 = 5.1666 29.8 is closer to 30 5.1666 is closer to 5 30/5 = 6 27 $\frac{8}{9}$ = 251/9 = 27.888 6 $\frac{5}{8}$ = 53/8 = 6.625 27.888 is closer to 30 6.625 is closer 7 30/7 = 5 6 > 5 $29 \frac{4}{5} \div 5 \frac{1}{6}$ > $27 \frac{8}{9} \div 6 \frac{5}{8}$

Question 12. $55 \frac{5}{6} \div 6 \frac{7}{10}$ _______ $11 \frac{5}{7} \div \frac{5}{8}$

Answer: $55 \frac{5}{6} \div 6 \frac{7}{10}$ < $11 \frac{5}{7} \div \frac{5}{8}$

Explanation: 55 $\frac{5}{6}$ = 335/6 = 55.833 6 $\frac{7}{10}$ = 67/10 = 6.7 55.833 is closer to 56 6.7 is closer to 7 56/7 = 8 11 $\frac{5}{7}$ = 82/7 = 11.714 $\frac{5}{8}$ = 0.625 11.714 is closer to 12 0.625 is closer to 1 12/1 = 12 8 < 12

Question 13. Marion is making school flags. Each flag uses 2 $\frac{3}{4}$ yards of felt. Marion has 24 $\frac{1}{8}$ yards of felt. About how many flags can he make? About _______ flags

Answer: About 8 flags

Explanation: Marion is making school flags. Each flag uses 2 $\frac{3}{4}$ yards of felt. Marion has 24 $\frac{1}{8}$ yards of felt. 2 $\frac{3}{4}$ = 11/4 24 $\frac{1}{8}$ = 193/8 193/8 ÷ 11/4 193/8 x 4/11 = 8.77 About 8 flags

Question 14. A garden snail travels about 2 $\frac{3}{5}$ feet in 1 minute. At that speed, about how many hours would it take the snail to travel 350 feet? About _______ hours

Answer: About 2 hours

Explanation: 2 $\frac{3}{5}$ = 2.6 That’s how long he travels in one minute. There are 60 minutes in an hour so multiply it by 60 and see if that gets you close to 350. 60 x 2.6 = 156 Now let’s add one more hour. 156 + 156 = 312 14 x 2.6 = 36.4 312 + 36.4 = 348.4 348.4 + 2.6 = 351 So two hours and fourteen minutes

Problem Solving + Applications – Page No. 104

What’s the Error?

Question 15. Megan is making pennants from a piece of butcher paper that is 10 $\frac{3}{8}$ yards long. Each pennant requires $\frac{3}{8}$ yard of paper. To estimate the number of pennants she could make, Megan estimated the quotient 10 $\frac{3}{8}$ ÷ $\frac{3}{8}$. Look at how Megan solved the problem. Find her error Estimate: 10 $\frac{3}{8}$ ÷ $\frac{3}{8}$ 10 ÷ $\frac{1}{2}$ = 5 Correct the error. Estimate the quotient. So, Megan can make about _____ pennants. Describe the error that Megan made Explain Tell which compatible numbers you used to estimate 10 $\frac{3}{8}$ ÷ $\frac{3}{8}$. Explain why you chose those numbers. Type below: __________

Answer: 10 $\frac{3}{8}$ ÷ $\frac{3}{8}$ 10 $\frac{3}{8}$ = 83/8 = 10.375 $\frac{3}{8}$ = 0.375 She had written 10 ÷ $\frac{1}{2}$ = 5 10.375 is closer to 10 0.375 is closer to 0.5 10/0.5 = 20 But she has written 5 instead of 20. Megan can make about 20 pennants.

For numbers 16a–16c, estimate to compare. Choose <, >, or =.

Question 16. 16a. 18 $\frac{3}{10} \div 2 \frac{5}{6}$ ? $30 \frac{7}{9} \div 3 \frac{1}{3}$ _____

Answer: 16a. 18 $\frac{3}{10} \div 2 \frac{5}{6}$ < $30 \frac{7}{9} \div 3 \frac{1}{3}$

Explanation: 18 $\frac{3}{10}$ = 183/10 = 18.3 2 $\frac{5}{6}$ = 17/6 = 2.833 18.3 is closer to 18 2.833 is closer to 3 18/3 = 6 30 $\frac{7}{9}$ = 277/9 = 30.777 3 $\frac{1}{3}$ = 10/3 = 3.333 30.777 is closer to 30 3.333 is closer to 3 30/3 = 10 6 < 10

Question 16. 16b. 17 $\frac{4}{5} \div 6 \frac{1}{6}$ ? $19 \frac{8}{9} \div 4 \frac{5}{8}$ _____

Answer: 17 $\frac{4}{5} \div 6 \frac{1}{6}$ < $19 \frac{8}{9} \div 4 \frac{5}{8}$

Explanation: 17 $\frac{4}{5}$ = 89/5 = 17.8 6 $\frac{1}{6}$ = 37/6 = 6.1666 17.8 is closer to 18 6.1666 is closer to 6 18/6 = 3 19 $\frac{8}{9}$ = 179/9 = 19.888 4 $\frac{5}{8}$ = 37/8 = 4.625 19.888 is closer to 20 4.625 is closer to 5 20/5 = 4 3 < 4 17 $\frac{4}{5} \div 6 \frac{1}{6}$ < $19 \frac{8}{9} \div 4 \frac{5}{8}$

Question 16. 16c. 17 $\frac{5}{6} \div 6 \frac{1}{4}$ ? $11 \frac{5}{7} \div 2 \frac{3}{4}$ _____

Answer: 17 $\frac{5}{6} \div 6 \frac{1}{4}$ < $11 \frac{5}{7} \div 2 \frac{3}{4}$

Explanation: 17 $\frac{5}{6}$ = 107/6 = 17.833 6 $\frac{1}{4}$ = 25/4 = 6.25 17.833 is closer to 18 6.25 is closer to 6 18/6 = 3 11 $\frac{5}{7}$ = 82/7 = 11.714 2 $\frac{3}{4}$ = 11/4 = 2.75 11.714 is closer to 12 2.75 is closer to 3 12/3 = 4 3 < 4 17 $\frac{5}{6} \div 6 \frac{1}{4}$ < $11 \frac{5}{7} \div 2 \frac{3}{4}$

Estimate Quotients – Page No. 105

Question 1. $12 \frac{3}{16} \div 3 \frac{9}{10}$ ______

Explanation: 12 $\frac{3}{16}$ = 195/16 = 12.1875 3 $\frac{9}{10}$ = 39/10 = 3.9 12.1875 is closer to 12 3.9 is closer to 4 12/4 = 3

Question 2. $15 \frac{3}{8} \div \frac{1}{2}$ ______

Explanation: 15 $\frac{3}{8}$ = 123/8 = 15.375 $\frac{1}{2}$ = 0.5 15.375 is closer to 15 0.5 is closer to 0.5 15/0.5 = 30

Question 3. $22 \frac{1}{5} \div 1 \frac{5}{6}$ ______

Explanation: 22 $\frac{1}{5}$ = 111/5 = 22.2 1 $\frac{5}{6}$ = 11/6 = 1.8333 22.2 is closer to 22 1.8333 is closer to 2 22/2 = 11

Question 4. $7 \frac{7}{9} \div \frac{4}{7}$ ______

Explanation: 7 $\frac{7}{9}$ = 70/9 = 7.777 $\frac{4}{7}$ = 0.571 7.777 is closer to 8 0.571 is closer to 0.5 8/0.5 = 16

Question 5. $18 \frac{1}{4} \div 2 \frac{4}{5}$ ______

Explanation: 18 $\frac{1}{4}$ = 73/4 = 18.25 2 $\frac{4}{5}$ = 14/5 = 2.8 18.25 is closer to 18 2.8 is closer to 3 18/3 = 6

Question 6. $\frac{15}{16} \div \frac{1}{7}$ ______

Explanation: $\frac{15}{16}$ = 0.9375 $\frac{1}{7}$ = 0.1428 0.9375 is closer to 1 0.1428 is closer to 0.1 1/0.1 = 10

Question 7. $14 \frac{7}{8} \div \frac{5}{11}$ ______

Explanation: 14 $\frac{7}{8}$ = 119/8 = 14.875 $\frac{5}{11}$ = 0.4545 14.875 is closer to 15 0.4545 is closer to 0.5 15/0.5 = 30

Question 8. $53 \frac{7}{12} \div 8 \frac{11}{12}$ ______

Explanation: 53 $\frac{7}{12}$ = 643/12 = 53.58 8 $\frac{11}{12}$ = 107/12 = 8.916 53.58 is closer to 54 8.916 is closer to 9 54/9 = 6

Question 9. $1 \frac{1}{6} \div \frac{1}{9}$ ______

Explanation: 1 $\frac{1}{6}$ = 7/6 = 1.166 $\frac{1}{9}$ = 0.111 1.166 is closer to 1 0.111 is closer to 0.1 1/0.1 = 10

Question 10. Estimate the number of pieces Sharon will have if she divides 15 $\frac{1}{3}$ yards of fabric into 4 $\frac{4}{5}$ yard lengths. About ______ pieces

Answer: About 3 pieces

Explanation: Sharon will have if she divides 15 $\frac{1}{3}$ yards of fabric into 4 $\frac{4}{5}$ yard lengths. 3 7/36 is the answer. So, about 3 pieces

Question 11. Estimate the number of $\frac{1}{2}$ quart containers Ethan can fill from a container with 8 $\frac{7}{8}$ quarts of water. About ______ containers

Answer: About 18 containers

Question 12. How is estimating quotients different from estimating products? Type below: __________

Answer: To estimate products and quotients, you need to first round the numbers. To round to the nearest whole number, look at the digit in the tenths place. If it is less than 5, round down. If it is 5 or greater, round up. Remember that an estimate is an answer that is not exact, but is approximate and reasonable. Let’s look at an example of estimating a product. Estimate the product: 11.256×6.81 First, round the first number. Since there is a 2 in the tenths place, 11.256 rounds down to 11. Next, round the second number. Since there is an 8 in the tenths place, 6.81 rounds up to 7. Then, multiply the rounded numbers. 11×7=77 The answer is 77. Let’s look at an example of estimating a quotient. Estimate the quotient: 91.93÷4.39 First, round the first number. Since there is a 9 in the tenths place, 91.93 rounds up to 92. Next, round the second number. Since there is a 3 in the tenths place, 4.39 rounds down to 4. Then, divide the rounded numbers. 92÷4=23 The answer is 23.

Lesson Check – Page No. 106

Question 1. Each loaf of pumpkin bread calls for 1 $\frac{3}{4}$ cups of raisins. About how many loaves can be made from 10 cups of raisins? About ______ loaves

Answer: About 5 loaves

Explanation: Divide 10 by 1 3/4. The answer is 5.714285 So you can make about 5 loaves of bread with 10 cups of raisins if each loaf needs 1 3/4 cups of raisins.

Question 2. Perry’s goal is to run 2 $\frac{1}{4}$ miles each day. One lap around the school track is $\frac{1}{3}$ mile. About how many laps must he run to reach his goal? About ______ laps

Answer: About 9 laps

Explanation: Perry’s goal is to run 2 $\frac{1}{4}$ miles each day. One lap around the school track is $\frac{1}{3}$ mile. 2 $\frac{1}{4}$ = 9/4 = 2.25 $\frac{1}{3}$ = 0.333 Perry will have to run 9 laps to reach his goal.

Question 3. A recipe calls for $\frac{3}{4}$ teaspoon of red pepper. Uri wants to use $\frac{1}{3}$ of that amount. How much red pepper should he use? $\frac{□}{□}$ teaspoon

Answer: $\frac{1}{4}$ teaspoon

Explanation: A recipe calls for $\frac{3}{4}$ teaspoon of red pepper. Uri wants to use $\frac{1}{3}$ of that amount. $\frac{1}{3}$ of $\frac{3}{4}$ = $\frac{1}{4}$

Question 4. A recipe calls for 2 $\frac{2}{3}$ cups of apple slices. Zoe wants to use 1 $\frac{1}{2}$ times this amount. How many cups of apples should Zoe use? ______ cups

Answer: 4 cups

Explanation: A recipe calls for 2 2/3 cups of apple slices. Zoe wants to use 1 1/2 times this amount. We will multiply the number of apple slices to 1 1/2 2 2/3 X 1 1/2 8/3 X3/2 = 24/6 = 4 cups Zoe will use 4 cups of apple slices.

Question 5. Edgar has 2.8 meters of rope. If he cuts it into 7 equal parts, how long will each piece be? ______ meters

Answer: 0.4 meters

Explanation: 2.8/7 = 0.4 meters

Question 6. Kami has 7 liters of water to fill water bottles that each hold 2.8 liters. How many bottles can she fill? ______ bottles

Answer: 2 bottles

Explanation: 7/2.8 = 2.5 she can only fill 2 because anything over that would 8.4 liters of water

Share and Show – Page No. 109

Estimate. Then find the quotient.

Question 1. $\frac{5}{6}$ ÷ 3 $\frac{□}{□}$

Explanation: 5/6 = 0.8333 is closer to 0.9 0.9/3 = 0.3 = 3/10

Use a number line to find the quotient.

Question 2. $\frac{3}{4} \div \frac{1}{8}$ _______

Explanation: 3/4 x 8 = 3 x 2 = 6

Question 3. $\frac{3}{5} \div \frac{3}{10}$ _______

Explanation: 3/5 x 10/3 = 2

Estimate. Then write the quotient in simplest form.

Question 4. $\frac{3}{4} \div \frac{5}{6}$ $\frac{□}{□}$

Answer: $\frac{1}{1}$

Explanation: 3/4 = 0.75 is closer to 0.8 5/6 = 0.8333 is closer to 0.8 0.8/0.8 = 1

Question 5. $3 \div \frac{3}{4}$ _______

Explanation: 3/4 = 0.75 3/0.75 = 4

Question 6. $\frac{1}{2} \div \frac{3}{4}$ $\frac{□}{□}$

Answer: $\frac{625}{1000}$

Explanation: 1/2 = 0.5 3/4 = 0.75 is closer to 0.8 0.5/0.8 = 0.625 = 625/1000

Question 7. $\frac{5}{12} \div 3$ $\frac{□}{□}$

Answer: $\frac{2}{10}$

Explanation: 5/12 = 0.4166 is closer to 0.6 0.6/3 = 0.2 = 2/10

Practice: Copy and Solve Estimate. Then write the quotient in simplest form

Question 8. $2 \div \frac{1}{8}$ _______

Explanation: 1/8 = 0.125 is closer to 0.1 2/0.1 = 20

Question 9. $\frac{3}{4} \div \frac{3}{5}$ $\frac{□}{□}$

Explanation: 3/4 = 0.75 is closer to 0.8 3/5 = is 0.6 closer to 0.8 0.8/0.8 = 1

Question 10. $\frac{2}{5} \div 5$ $\frac{□}{□}$

Explanation: 2/5 = 0.4 is closer to 0.5 0.5/5 = 0.1 = 1/10

Question 11. $4 \div \frac{1}{7}$ _______

Explanation: 1/7 = 0.1428 is closer to 0.1 4/0.1 = 40

Practice: Copy and Solve Evaluate using the order of operations.

Question 12. $\left(\frac{3}{5}+\frac{1}{10}\right) \div 2$ $\frac{□}{□}$

Answer: $\frac{7}{20}$

Explanation: 3/5 + 1/10 = 7/10 = 0.7 0.7/2 = 7/20

Question 13. $\frac{3}{5}+\frac{1}{10} \div 2$ $\frac{□}{□}$

Answer: $\frac{13}{20}$

Explanation: $\frac{3}{5}+\frac{1}{10} \div 2$ (1/10)/2 = 1/20 3/5 + 1/20 = 0.65 = 13/20

Question 14. $\frac{3}{5}+2 \div \frac{1}{10}$ _______ $\frac{□}{□}$

Explanation: 2/(1/10) = 1/5 3/5 + 1/5 = 4/5

Question 15. Generalize Suppose the divisor and the dividend of a division problem are both fractions between 0 and 1, and the divisor is greater than the dividend. Is the quotient less than, equal to, or greater than 1? Type below: __________

Answer: Divisor and Dividend are fractions lying between 0 and 1 Also, Divisor > Dividend A smaller number is being divided by a larger number Whenever a smaller number is divided by a larger number, the quotient is less than 1 Example: 0,5/0,6 Here, they are both numbers between 0 and 1, and the divisor is greater than the dividend. The result is 0,8333, LESS THAN 1 Hence, the answer is that the quotient will be less than 1

Problem Solving + Applications – Page No. 110

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 16$

Question 16. Kristen wants to cut ladder rungs from a 6 ft board. How many ladder rungs can she cut? _______ ladder rungs

Answer: 8 ladder rungs

Explanation: Kristen wants to cut ladder rungs from a 6 ft board. ladder rungs = 3/4 ft 6/(3/4) = 8 rungs

Question 17. Pose a Problem Look back at Problem 16. Write and solve a new problem by changing the length of the board Kristen is cutting for ladder rungs. Type below: __________

Answer: Kristen wants to cut ladder rungs from a 9 ft board. How many ladder rungs can she cut? Kristen wants to cut ladder rungs from a 9 ft board. ladder rungs = 3/4 ft 9/(3/4) = 12 rungs

Question 18. Dan paints a design that has 8 equal parts along the entire length of the windowsill. How long is each part of the design? $\frac{□}{□}$ yards

Answer: $\frac{1}{16}$ yards

Explanation: Dan paints a design that has 8 equal parts along the entire length of the windowsill. (1/2)/8 = 1/2 x 1/8 = 1/16 yards

Question 19. Dan has a board that is $\frac{15}{16}$ yd. How many “Keep Out” signs can he make if the length of the sign is changed to half of the original length? _______ signs

Answer: 3 signs

Explanation: Dan has a board that is $\frac{15}{16}$ yd. If the length of the sign is changed to half of the original length, (5/8)/2 = 5/16 (15/16) ÷ 5/16 = 15/16 x 16/5 = 3

Question 20. Lauren has $\frac{3}{4}$ cup of dried fruit. She puts the dried fruit into bags, each holding $\frac{1}{8}$ cup. How many bags will Lauren use? Explain your answer using words and numbers. Type below: __________

Explanation: Lauren has $\frac{3}{4}$ cup of dried fruit. She puts the dried fruit into bags, each holding $\frac{1}{8}$ cup. 3/4 ÷ 1/8 = 3/4 x 8 = 6 Lauren has 3/4 and in 1/4 there are 2 1/8s. That 3 fourths times two = 6 so 6 one eights

Divide Fractions – Page No. 111

Question 1. $5 \div \frac{1}{6}$ _____

Explanation: 1/6 = 0.166 is closer to 0.2 5/0.2 = 25

Question 2. $\frac{1}{2} \div \frac{1}{4}$ _____

Explanation: 1/2 = 0.5 is closer to 1 1/4 = 0.25 is closer to 0.2 1/0.2 = 5

Question 3. $\frac{4}{5} \div \frac{2}{3}$ _____ $\frac{□}{□}$

Answer: 1 $\frac{1}{5}$

Explanation: 4/5 = 0.8 is closer to 0.8 2/3 = 0.66 is closer to 0.6 0.8/0.6 = 1 1/5

Question 4. $\frac{14}{15} \div 7$ $\frac{□}{□}$

Answer: $\frac{2}{15}$

Explanation: 14/15 = 0.9333 0.9/7 = 2/15

Question 5. $8 \div \frac{1}{3}$ _____

Explanation: 1/3 = 0.33 is closer to 0.4 8/0.4 = 20

Question 6. $\frac{12}{21} \div \frac{2}{3}$ $\frac{□}{□}$

Explanation: 12/21 = 0.571 is closer to 0.6 2/3 = 0.666 is closer to 0.6 0.6/0.6 = 1

Question 7. $\frac{5}{6} \div \frac{5}{12}$ _____

Explanation: 5/6 = 0.833 is closer to 0.8 5/12 = 0.416 is closer to 0.4 0.8/0.4 = 2

Question 8. $\frac{5}{8} \div \frac{1}{2}$ _____ $\frac{□}{□}$

Answer: 1 $\frac{2}{10}$

Explanation: 5/8 = 0.625 is closer to 0.6 1/2 = 0.5 is closer to 0.5 0.6/0.5 = 1.2 = 1 2/10

Question 9. Joy ate $\frac{1}{4}$ of a pizza. If she divides the rest of the pizza into pieces equal to $\frac{1}{8}$ pizza for her family, how many pieces will her family get? _____ pieces

Answer: 6 pieces

Explanation: The pizza is divided into 4 pieces, Joy ate 1/4. So, the left pices are 1 – 1/4 = 3/4 now, 3/4 of a pizza and Joy will divide this rest of the pizza in pieces equal to 1/8, so we need to make a division (3/4) ÷ (1/8) = 24/4 = 6 pieces.

Question 10. Hideko has $\frac{3}{5}$ yard of ribbon to tie on balloons for the festival. Each balloon will need $\frac{3}{10}$ yard of ribbon. How many balloons can Hideko tie with ribbon? _____ balloons

Answer: 2 balloons

Explanation: 3/10 yard of ribbon required to tie = 1 balloon 3/5 yard of ribber can tie = (3/5) ÷ (3/10) = 2 ballons With 3/5 yard, Hideko can tie 2 balloons

Question 11. Rick knows that 1 cup of glue weighs $\frac{1}{18}$ pound. He has $\frac{2}{3}$ pound of glue. How many cups of glue does he have? _____ cups

Answer: 12 cups

Explanation: For 1/18lb, 1 cup For 2/3lb, x cups. 1/8x = 1 x 2/3 1/8x = 2/3 x = 2/3 x 18 x = 2 x 6 = 12 cups

Question 12. Mrs. Jennings had $\frac{5}{7}$ gallon of paint. She gave $\frac{1}{7}$ gallon each to some students. How many students received paint if Mrs. Jennings gave away all the paint? _____ students

Answer: 4 students

Explanation: Mrs. Jennings had $\frac{5}{7}$ gallon of paint. She gave $\frac{1}{7}$ gallon each to some students. $\frac{5}{7}$ ÷ $\frac{1}{7}$ = 25/7 = 3.571 is closer to 4

Question 13. Write a word problem that involves two fractions. Include the solution. Type below: __________

Answer: Mrs. Jennings had $\frac{5}{7}$ gallon of paint. She gave $\frac{1}{7}$ gallon each to some students. How many students received paint if Mrs. Jennings gave away all the paint? Answer: Mrs. Jennings had $\frac{5}{7}$ gallon of paint. She gave $\frac{1}{7}$ gallon each to some students. $\frac{5}{7}$ ÷ $\frac{1}{7}$ = 25/7 = 3.571 is closer to 4

Lesson Check – Page No. 112

Question 1. There was $\frac{2}{3}$ of a pizza for 6 friends to share equally. What fraction of the pizza did each person get? $\frac{□}{□}$

Explanation: There was $\frac{2}{3}$ of a pizza for 6 friends to share equally. $\frac{2}{3}$ ÷ 6 = 2/3 x 1/6 = 2/18 = 1/9

Question 2. Rashad needs $\frac{2}{3}$ pound of wax to make a candle. How many candles can he make with 6 pounds of wax? _____ candles

Answer: 9 candles

Explanation: Rashad needs 2/3 pound a wax to make candles. 1 Candle = 2/3 pounds. So, for 2 pounds, 3 x 2/3 = 3 candles 2 pounds = 3 candles 1 pound = 3/2 candles So, for 6 pounds, 6 x 3/2 = 9 candles

Question 3. Jeremy had $\frac{3}{4}$ of a submarine sandwich and gave his friend $\frac{1}{3}$ of it. What fraction of the sandwich did the friend receive? $\frac{□}{□}$

Explanation: Jeremy had $\frac{3}{4}$ of a submarine sandwich and gave his friend $\frac{1}{3}$ of it. 1/3 x 3/4 = 1/4

Question 4. Ebony walked at a rate of 3 $\frac{1}{2}$ miles per hour for 1 $\frac{1}{3}$ hours. How far did she walk? _____ $\frac{□}{□}$

Answer: 4 $\frac{2}{3}$

Explanation: Ebony walked at a rate of 3 $\frac{1}{2}$ miles per hour for 1 $\frac{1}{3}$ hours. 3 1/2 miles = 7/2 miles … 1 hour x miles = ? … 1 1/3 hours = 4/3 hours 7/2 x 4/3 = 1 x x x = 7/2 x 4/3 x = 14/3 = 4 2/3 miles The correct result would be 4 2/3 miles.

Question 5. Penny uses $\frac{3}{4}$ yard of fabric for each pillow she makes. How many pillows can she make using 6 yards of fabric? _____ pillows

Answer: 8 pillows

Explanation: Penny uses $\frac{3}{4}$ yard of fabric for each pillow she makes. Using 6 yards of fabric 6/(3/4) = 24/3 = 8

Question 6. During track practice, Chris ran 2.5 laps in 81 seconds. What was his average time per lap? _____ seconds

Answer: 32.4 seconds

Explanation: During track practice, Chris ran 2.5 laps in 81 seconds. 81/2.5 = 32.4 seconds

Share and Show – Page No. 115

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 17$

Explanation: Model 3 with 3 hexagonal blocks. Model 1/2 with 1 trapezoid block. For 1/6, 6 triangle blocks are equal to 1 hexagon. So, a triangle block shows 1/6. Count the triangles. There are 21 triangle blocks. So, 3 1/2 ÷ 1/6 = 21.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 18$

Explanation: Model 2 with 2 hexagonal blocks. Model 1/2 with 1 trapezoid block. For 1/6, 6 triangle blocks are equal to 1 hexagon. So, a triangle block shows 1/6. Count the triangles. There are 15 triangle blocks. So, $2 \frac{1}{2} \div \frac{1}{6}$ = 15.

Use pattern blocks to find the quotient. Then draw the model.

Question 3. $2 \frac{2}{3} \div \frac{1}{6}$ _____

Explanation: 2 2/3 = 8/3 8/3 ÷ 1/6 = 16

Question 4. $3 \frac{1}{2} \div \frac{1}{2}$ _____

Explanation: 3 1/2 = 7/2 7/2 ÷ 1/2 = 7

Draw a model to find the quotient.

Question 5. $3 \frac{1}{2} \div 3$ _____ $\frac{□}{□}$

Explanation: 3 1/2 = 7/2 7/2 ÷ 3 = 21/2

Question 6. $1 \frac{1}{4} \div 2$ $\frac{□}{□}$

Explanation: 1/4 ÷ 2 = 1/2

Question 7. Use Appropriate Tools Explain how models can be used to divide mixed numbers by fractions or whole numbers Type below: __________

Answer: Multiply the whole number part by the fraction’s denominator. Add that to the numerator. Then write the result on top of the denominator.

Problem Solving + Applications – Page No. 116

Use a model to solve. Then write an equation for the model.

Question 8. Use Models Eliza opens a box of bead kits. The box weighs 2 $\frac{2}{3}$ lb. Each bead kit weighs $\frac{1}{6}$ lb. How many kits are in the box? What does the answer mean? Type below: __________

Explanation: Eliza opens a box of bead kits. The box weighs 2 $\frac{2}{3}$ lb. Each bead kit weighs $\frac{1}{6}$ lb, 2 $\frac{2}{3}$ ÷ $\frac{1}{6}$ = 8/3 ÷ 1/6 = 16. 16 kits are in the box

Question 9. Hassan has two boxes of trail mix. Each box holds 1 $\frac{2}{3}$ lb of trail mix. He eats $\frac{1}{3}$ lb of trail mix each day. How many days can Hassan eat trail mix before he runs out? _____ days

Answer: 10 days

Explanation: Hassan has two boxes of trail mix. Each box holds 1 $\frac{2}{3}$ lb of trail mix. 1 $\frac{2}{3}$ = 5/3 2 x (5/3) = 10/3 He eats $\frac{1}{3}$ lb of trail mix each day. 10/3 ÷ 1/3 = 10 Hassan eats trail mix for 10 days before he runs out.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 19$

Answer: $2 \frac{1}{3} \div \frac{1}{6}$ = 7/3 ÷ 1/6 = 14. He said the quotient is 7. His answer is Nonsense.

Question 11. Eva is making muffins to sell at a fundraiser. She has 2 $\frac{1}{4}$ cups of flour, and the recipe calls for $\frac{3}{4}$ cup of flour for each batch of muffins. Explain how to use a model to find the number of batches of muffins Eva can make. Type below: __________

Explanation: Eva is making muffins to sell at a fundraiser. She has 2 $\frac{1}{4}$ cups of flour, and the recipe calls for $\frac{3}{4}$ cup of flour for each batch of muffins. 2 $\frac{1}{4}$ ÷ $\frac{3}{4}$ = 9/4 ÷ 3/4 = 3

Model Mixed Number Division – Page No. 117

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 20$

Explanation: Count the number of trapezoids to find the answer.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 21$

Use pattern blocks or another model to find the quotient. Then draw the model.

Question 3. $2 \frac{1}{2} \div \frac{1}{6}$ _____

Question 4. $2 \frac{3}{4} \div 2$ _____

Explanation: 2 3/4 ÷ 2 = 11/2

Question 5. Marty has 2 $\frac{4}{5}$ quarts of juice. He pours the same amount of juice into 2 bottles. How much does he pour into each bottle? _____ $\frac{□}{□}$ quarts

Answer: 1$\frac{2}{5}$ quarts

Explanation: Marty has 2 $\frac{4}{5}$ quarts of juice. He pours the same amount of juice into 2 bottles. 2 $\frac{4}{5}$ = 14/5 = 2.8 2.8/2 = 1.4 = 1 2/5

Question 6. How many $\frac{1}{3}$ pound servings are in 4 $\frac{2}{3}$ pounds of cheese? _____ pounds

Answer: 14 pounds

Explanation: 4 2/3 = 14/3 (14/3)/(1/3) = 14

Question 7. Write a word problem that involves dividing a mixed number by a whole number. Solve the problem and describe how you found the answer. Type below: __________

Answer: How many $\frac{1}{3}$ pound servings are in 4 $\frac{2}{3}$ pounds of cheese? Explanation: 4 2/3 = 14/3 (14/3)/(1/3) = 14

Lesson Check – Page No. 118

Sketch a model to find the quotient.

Question 1. Emma has 4 $\frac{1}{2}$ pounds of birdseed. She wants to divide it evenly among 3 bird feeders. How much birdseed should she put in each? _____ $\frac{□}{□}$ pounds

Answer: 1$\frac{1}{2}$ pounds

Explanation: Emma has 4 1/2 pounds of birdseed. Convert this to an improper fraction. 4 1/2 = 9/2 Emma wants to divide it evenly among 3 bird feeders. So, she should put (9/2)/3 = 3/2 = 1 1/2

Question 2. A box of crackers weighs 11 $\frac{1}{4}$ ounces. Kaden estimates that one serving is $\frac{3}{4}$ ounce. How many servings are in the box? _____ servings

Answer: 15 servings

Explanation: 11 1/4 by 3/4 11 1/4 = 45/4 45/4 / 3/4 = 45/4 × 4/3 = 180/12 = 15 there are 15 servings

Question 3. The Ecology Club has volunteered to clean up 4.8 kilometers of highway. The members are organized into 16 teams. Each team will clean the same amount of highway. How much highway will each team clean? _____ kilometers

Answer: 0.3 kilometers

Explanation: The Ecology Club has volunteered to clean up 4.8 kilometers of highway. The members are organized into 16 teams. The total length of the highway is given to clean = 4.8 kilometers If the members are organized into 16 teams. 4.8/16 = 0.3 Hence, each team will clean 0.3 kilometers of the highway.

Question 4. Tyrone has $8.06. How many bagels can he buy if each bagel costs $0.65? _____ bagels

Answer: 12 bagels

Explanation: $8.06/$0.65 = 12.4 12 bagels

Question 5. A nail is 0.1875 inch thick. What is its thickness as a fraction? Is 0.1875 inch closer to $\frac{1}{8}$ inch or $\frac{1}{4}$ inch on a number line? Type below: __________

Answer: 0.1875 = 3/16 which is at the same distance to 1/4 and 1/8 It is the same distance apart.

Question 6. Maria wants to find the product of 5 $\frac{3}{20}$ × 3 $\frac{4}{25}$ using decimals instead of fractions. How can she rewrite the problem using decimals? Type below: __________

Answer: 16.274

Explanation: The decimal for 5 3/20 is 5.15 The decimal for 3 4/25 is 3.16 5.15 × 3.16 = 16.274

Share and Show – Page No. 121

Question 1. $4 \frac{1}{3} \div \frac{3}{4}$ ______ $\frac{□}{□}$

Answer: 5$\frac{375}{1000}$

Explanation: 4 1/3 = 13/3 = 4.333 is closer to 4.3 3/4 = 0.75 is closer to 0.8 4.3/0.8 = 5.375 = 5 375/1000

Question 2. Six hikers shared 4 $\frac{1}{2}$ lb of trail mix. How much trail mix did each hiker receive? $\frac{□}{□}$

Answer: $\frac{75}{100}$

Explanation: 6 hikers = 4.5 lbs of trail mix 4.5/6= .75 lbs each hiker.

Question 3. $5 \frac{2}{3} \div 3$ ______ $\frac{□}{□}$

Answer: 2$\frac{947}{1000}$

Explanation: 5 2/3 = 17/3 = 5.666 is closer to 5.6 5.6/3 = 1.866 is closer to 1.9 5.6/1.9 = 2.947 = 2 947/1000

Question 4. $7 \frac{1}{2} \div 2 \frac{1}{2}$ ______

Explanation: 7 1/2 = 15/2 = 7.5 2 1/2 = 5/2 = 2.5 7.5/2.5 = 3

Question 5. $5 \frac{3}{4} \div 4 \frac{1}{2}$ ______ $\frac{□}{□}$

Answer: 1$\frac{27}{100}$

Explanation: 5 3/4 = 23/4 = 5.75 4 1/2 = 9/2 = 4.5 5.75/4.5 = 1.27 = 1 27/100

Question 6. $5 \div 1 \frac{1}{3}$ ______ $\frac{□}{□}$

Answer: 3$\frac{84}{100}$

Explanation: 1 1/3 = 4/3 = 1.33 is closer to 1.3 5/1.3 = 3.84 = 3 84/100

Question 7. $6 \frac{3}{4} \div 2$ ______ $\frac{□}{□}$

Answer: 3$\frac{2}{5}$

Explanation: 6 3/4 = 27/4 = 6.75 is closer to 6.8 6.8/2 = 3.4 = 3 2/5

Question 8. $2 \frac{2}{9} \div 1 \frac{3}{7}$ ______ $\frac{□}{□}$

Answer: 1$\frac{571}{1000}$

Explanation: 2 2/9 = 20/9 = 2.22 is closer to 2.2 1 3/7 = 10/7 = 1.428 is closer to 1.4 2.2/1.4 = 1.571 = 1 571/1000

Question 9. How many 3 $\frac{1}{3}$ yd pieces can Amanda get from a 3 $\frac{1}{3}$ yd ribbon? ______

Explanation: (3 1/3) ÷ (3 1/3) = 1

Question 10. Samantha cut 6 $\frac{3}{4}$ yd of yarn into 3 equal pieces. Explain how she could use mental math to find the length of each piece Type below: __________

Answer: 27/12

Explanation: Samantha cut 6 $\frac{3}{4}$ yd of yarn into 3 equal pieces. 6 3/4 = 27/4 (27/4)/3 (27/4)(1/3) = 27/12

Evaluate Algebra Evaluate using the order of operations. Write the answer in simplest form.

Question 11. $1 \frac{1}{2} \times 2 \div 1 \frac{1}{3}$ _____ $\frac{□}{□}$

Answer: 2$\frac{1}{4}$

Explanation: (1 1/2) × 2 = 3/2 × 2 = 3 1 1/3 = 4/3 3/(4/3) = 9/4 = 2.25 = 2 1/4

Question 12. $1 \frac{2}{5} \div 1 \frac{13}{15}+\frac{5}{8}$ _____ $\frac{□}{□}$

Answer: 1$\frac{3}{8}$

Explanation: (1 2/5)/(1 13/15) = (7/5)/(28/15) = 3/4 = 0.75 0.75 + 0.625 = 1.375 = 1 3/8

Question 13. $3 \frac{1}{2}-1 \frac{5}{6} \div 1 \frac{2}{9}$ _____

Explanation: (1 5/6)/(1 2/9) = (11/6)/11/9 = 3/2 = 1 1/2 = 1.5 3 1/2 = 7/2 = 3.5 3.5 – 1.5 = 2

Question 14. Look for a Pattern Find these quotients: $20 \div 4 \frac{4}{5}$, $10 \div 4 \frac{4}{5}$, $5 \div 4 \frac{4}{5}$. Describe a pattern you see. Type below: __________

Answer: 20 ÷ 4 4/5 = 20 ÷ 24/5 = 20/4.8 = 4.1666 10 ÷ 4 4/5 = 10 ÷ 24/5 = 10/4.8 = 2.08333 5 ÷ 4 4/5 = 5 ÷ 24/5 = 5/4.8 = 1.04166 The pattern is multiplied by 2 every time.

Page No. 122

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 22$

Answer: How many breaks Dina will take when hikes $\frac{1}{2}$ of the easy trail and stops for a break every 3 $\frac{1}{4}$ mile.

Question 15. b. How will you use the information in the table to solve the problem? Type below: __________

Answer: Dina easy trail length, break time

Question 15. c. How can you find the distance Dina hikes? How far does she hike? ______ $\frac{□}{□}$ miles

Answer: 9$\frac{3}{4}$ miles

Explanation: 19 1/2 × 1/2 = 39/2 × 1/2 = 39/4 = 9 3/4

Question 15. d. What operation will you use to find how many breaks Dina takes? Type below: __________

Answer: Division

Question 15. e. How many breaks will Dina take? ______ breaks

Answer: 3 breaks

Explanation: 39/4 ÷ 13/4 = 3

Question 16. Carlo packs 15 $\frac{3}{4}$ lb of books in 2 boxes. Each book weighs 1 $\frac{1}{8}$ lb. There are 4 more books in Box A than in Box B. How many books are in Box A? Explain your work. ______ books

Answer: Carlo packs 15 $\frac{3}{4}$ lb of books in 2 boxes. Each book weighs 1 $\frac{1}{8}$ lb. 15 $\frac{3}{4}$ ÷ 1 $\frac{1}{8}$ = 63/4 ÷ 9/8 = 14 14 books available in 2 boxes. There are 4 more books in Box A than in Box B. Box A contains 5 + 4 = 9 books Box B contains 5 books

Question 17. Rex’s goal is to run 13 $\frac{3}{4}$ miles over 5 days. He wants to run the same distance each day. Jordan said that Rex would have to run 3 $\frac{3}{4}$ miles each day to reach his goal. Do you agree with Jordan? Explain your answer using words and numbers. Type below: __________

Answer: Rex’s goal is to run 13 $\frac{3}{4}$ miles over 5 days. He wants to run the same distance each day. 13 $\frac{3}{4}$ ÷ 5 = 55/4 ÷ 5 = 11/4 or 2 3/4. Jordan answer is wrong

Divide Mixed Numbers – Page No. 123

Question 1. $2 \frac{1}{2} \div 2 \frac{1}{3}$ ______ $\frac{□}{□}$

Answer: 1$\frac{1}{2}$

Explanation: 2 1/2 = 5/2 = 2.5 is closer to 3 2 1/3 = 7/3 = 2.333 is closer to 2 3/2 = 1.5 = 1 1/2

Question 2. $2 \frac{2}{3} \div 1 \frac{1}{3}$ ______

Explanation: 2 2/3 = 8/3 = 2.666 is closer to 2.6 1 1/3 = 4/3 = 1.333 is closer to 1.3 2.6/1.3 = 2

Question 3. $2 \div 3 \frac{5}{8}$ $\frac{□}{□}$

Explanation: 3 5/8 = 29/8 = 3.625 is closer to 3.6 2/3.6 = 0.5 = 1/2

Question 4. $1 \frac{13}{15} \div 1 \frac{2}{5}$ $\frac{□}{□}$

Answer: $\frac{126}{100}$

Explanation: 1 13/15 = 28/15 = 1.8666 is closer to 1.9 1 2/5 = 7/5 = 1.4 is closer to 1.5 1.9/1.5 = 1.266 126/100

Question 5. $10 \div 6 \frac{2}{3}$ ______ $\frac{□}{□}$

Explanation: 6 2/3 = 20/3 = 6.666 is closer to 6.7 10/6.7 = 3/2 = 1 1/2

Question 6. $2 \frac{3}{5} \div 1 \frac{1}{25}$ ______ $\frac{□}{□}$

Answer: 2$\frac{3}{5}$

Explanation: 2 3/5 = 13/5 = 2.6 1 1/25 = 26/25 = 1.04 is closer to 1 2.6/1 = 13/5 or 2 3/5

Question 7. $2 \frac{1}{5} \div 2$ ______ $\frac{□}{□}$

Answer: 1$\frac{1}{10}$

Explanation: 2 1/5 = 11/5 = 2.2 is closer to 2.2 2.2/2 = 1.1 = 11/10 = 1 1/10

Question 8. Sid and Jill hiked 4 $\frac{1}{8}$ miles in the morning and 1 $\frac{7}{8}$ miles in the afternoon. How many times as far did they hike in the morning as in the afternoon? ______ $\frac{□}{□}$ times

Answer: 2$\frac{1}{5}$ times

Explanation: Sid and Jill hiked 4 $\frac{1}{8}$ miles in the morning and 1 $\frac{7}{8}$ miles in the afternoon. 4 $\frac{1}{8}$ = 33/8 1 $\frac{7}{8}$ = 15/8 (33/8) ÷ (15/8) = 33/15 = 11/5 or 2 1/5

Question 9. It takes Nim 2 $\frac{2}{3}$ hours to weave a basket. He worked Monday through Friday, 8 hours a day. How many baskets did he make? ______ baskets

Answer: 15 baskets

Explanation: he worked (Mon – Fri) 5 days at 8 hrs per day = 5 × 8= 40 hrs 40/ (2 2/3) = 40 / (8/3) = 40 × 3/8 = 120/8 = 15 baskets

Question 10. A tree grows 1 $\frac{3}{4}$ feet per year. How long will it take the tree to grow from a height of 21 $\frac{1}{4}$ feet to a height of 37 feet? ______ years

Answer: 9 years

Explanation: A tree grows 1 3/4 = 7/4 feet per year. If you would like to know how long will it take the tree to grow from a height of 21 1/4 = 85/4 feet to a height of 37 feet, 37 – 21 1/4 = 37 – 85/4 = 148/4 – 85/4 = 63/4 = 15 3/4 15 3/4 / 1 3/4 = 63/4 / 7/4 = 63/4 × 4/7 = 9 years

Question 11. Explain how you would find how many 1 $\frac{1}{2}$ cup servings there are in a pot that contains 22 $\frac{1}{2}$ cups of soup. Type below: __________

Answer: Given that, Total number of cups = 22 1/2 The number of cups required for each serving = 1 1/2 The number of servings = 22 1/2 ÷ 1 1/2 = 45/2 ÷ 3/2 = 45/3 = 15

Lesson Check – Page No. 124

Question 1. Tom has a can of paint that covers 37 $\frac{1}{2}$ square meters. Each board on the fence has an area of $\frac{3}{16}$ square meters. How many boards can he paint? ______ boards

Answer: 200 boards

Explanation: Tom has a can of paint that covers 37 $\frac{1}{2}$ square meters. Each board on the fence has an area of $\frac{3}{16}$ square meters. 37 $\frac{1}{2}$ ÷ $\frac{3}{16}$ = 200 square meters

Question 2. A baker wants to put 3 $\frac{3}{4}$ pounds of apples in each pie she makes. She purchased 52 $\frac{1}{2}$ pounds of apples. How many pies can she make? ______ pies

Answer: 14 pies

Explanation: A baker wants to put 3 $\frac{3}{4}$ pounds of apples in each pie she makes. She purchased 52 $\frac{1}{2}$ pounds of apples. 52 $\frac{1}{2}$ ÷ 3 $\frac{3}{4}$ = 14 pies

Question 3. The three sides of a triangle measure 9.97 meters, 10.1 meters, and 0.53 meter. What is the distance around the triangle? ______ meters

Answer: 20.6 meters

Explanation: The distance around the triangle is call perimeter, to get it we must add the 3 sides. So, 9.97 + 10.1 + 0.53 = 20.6 meters

Question 4. Selena bought 3.75 pounds of meat for $4.64 per pound. What was the total cost of the meat? $ ______

Answer: $17.40

Explanation: Selena bought 3.75 pounds of meat. The cost of meat of one pound = $4.64 The total cost of the meat = 4.64 × 3.75 = $17.40 The total cost of 3.75 lb of meat was $17.40.

Question 5. Melanie prepared 7 $\frac{1}{2}$ tablespoons of a spice mixture. She uses $\frac{1}{4}$ tablespoon to make a batch of barbecue sauce. Estimate the number of batches of barbecue sauce she can make using the spice mixture. Type below: __________

Answer: 30 batches of sauce

Explanation: Melanie prepared 7 $\frac{1}{2}$ tablespoons of a spice mixture. She uses $\frac{1}{4}$ tablespoon to make a batch of barbecue sauce. 4 X 1/4 tbsp = 1 tbsp. 4 X 7 1/2 = 30. she can make 30 batches of sauce

Question 6. Arturo mixed together 1.24 pounds of pretzels, 0.78 pounds of nuts, 0.3 pounds of candy, and 2 pounds of popcorn. He then packaged it in bags that each contained 0.27 pounds. How many bags could he fill? ______ bags

Answer: 16 bags

Explanation: Arturo mixed together 1.24 pounds of pretzels, 0.78 pounds of nuts, 0.3 pounds of candy, and 2 pounds of popcorn. 1.24 + 0.78 + 0.3 + 2 = 4.32 4.32/0.27 = 16

Page No. 127

Question 1. There is $\frac{4}{5}$ lb of sand in the class science supplies. If one scoop of sand weighs $\frac{1}{20}$ lb, how many scoops of sand can Maria get from the class supplies and still leave $\frac{1}{2}$ lb in the supplies? Type below: __________

Answer: 16 scoops

Explanation: There is $\frac{4}{5}$ lb of sand in the class science supplies. If one scoop of sand weighs $\frac{1}{20}$ lb, $\frac{4}{5}$ ÷ $\frac{1}{20}$ = 4/5 × 1/20 = 16 scoops

Question 2. What if Maria leaves $\frac{2}{5}$ lb of sand in the supplies? How many scoops of sand can she get? ______ scoops

Answer: 8 scoops

Explanation: There is $\frac{2}{5}$ lb of sand in the class science supplies. If one scoop of sand weighs $\frac{1}{20}$ lb, $\frac{2}{5}$ ÷ $\frac{1}{20}$ = 2/5 × 20 = 8

Question 3. There are 6 gallons of distilled water in the science supplies. If 10 students each use an equal amount of the distilled water and there is 1 gal left in the supplies, how much will each student get? $\frac{□}{□}$ gallon

Answer: $\frac{1}{2}$ gallon

Explanation: There are 6 gallons of distilled water in the science supplies. There is 1 gal left in the supplies, 6 – 1 = 5 10 students each use an equal amount of the distilled water = 5/10 = 1/2 .5 gal for each student

On Your Own – Page No. 128

Question 4. The total weight of the fish in a tank of tropical fish at Fish ‘n’ Fur was $\frac{7}{8}$ lb. Each fish weighed $\frac{1}{64}$ lb. After Eric bought some fish, the total weight of the fish remaining in the tank was $\frac{1}{2}$ lb. How many fish did Eric buy? ______ fish

Answer: 386 fish

Explanation: The total weight of the fish in a tank of tropical fish at Fish ‘n’ Fur was $\frac{7}{8}$ lb. Each fish weighed $\frac{1}{64}$ lb. After Eric bought some fish, the total weight of the fish remaining in the tank was $\frac{1}{2}$ lb. 386 is the answer

Question 5. Fish ‘n’ Fur had a bin containing 2 $\frac{1}{2}$ lb of gerbil food. After selling bags of gerbil food that each held $\frac{3}{4}$ lb, $\frac{1}{4}$ lb of food was left in the bin. If each bag of gerbil food sold for $3.25, how much did the store earn? $ ______

Answer: $9.75

Explanation: The store would earn 9.75$ because 3 bags of gerbil food is sold. Then you would multiply 3 by 3.25.

Question 6. Describe Niko bought 2 lb of dog treats. He gave his dog $\frac{3}{5}$ lb of treats one week and $\frac{7}{10}$ lb of treats the next week. Describe how Niko can find how much is left. Type below: __________

Answer: Niko bought 2 lb of dog treats. He gave his dog $\frac{3}{5}$ lb of treats one week and $\frac{7}{10}$ lb of treats the next week. Let us find the amount of dog-food eaten by dogs in two months. 3/5 + 7/10 = 13/10 Now we will subtract the amount of food eaten by the dog from the amount of food initially to find the remaining amount of dog food. 2 – 13/10 = 7/10 Therefore, 7/10 pounds of food was remaining in the bag at the end of the two months.

Question 7. There were 14 $\frac{1}{4}$ cups of apple juice in a container. Each day, Elise drank 1 $\frac{1}{2}$ cups of apple juice. Today, there is $\frac{3}{4}$ cup of apple juice left. Derek said that Elise drank apple juice on nine days. Do you agree with Derek? Use words and numbers to explain your answer. Type below: __________

Answer: Derek is correct.

Explanation: An apple juice the container had 14 1/2 =14.25 She drank per day 1 1/2= 1.5 The left part in the container 3/4= .75 14.25 cups – .75 cup = 13.5 cups 13.5 cups ÷ 1.5 cups per day= 9 days

Problem Solving Fraction Operations – Page No. 129

Read each problem and solve.

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 23$

Answer: 9 friends

Explanation: Let us say that there are x friends. Each one gets 1/18 of the original pizza: but this in turn leaves 1/6 of the 2/3 leftover. 1x/18 = 2/3 – 1/6 x = 12 – 3 = 9

Question 2. Sarah’s craft project uses pieces of yarn that are $\frac{1}{8}$ yard long. She has a piece of yarn that is 3 yards long. How many $\frac{1}{8}$ -yard pieces can she cut and still have 1 $\frac{1}{4}$ yards left? ______ pieces

Answer: 14 pieces

Explanation: Sarah’s craft project uses pieces of yarn that are $\frac{1}{8}$ yard long. She has a piece of yarn that is 3 yards long. If she left 1 $\frac{1}{4}$ yards left, 3 – 1 $\frac{1}{4}$ = 7/4 7/4 ÷ $\frac{1}{8}$ = 14

Question 3. Alex opens a 1-pint container of orange butter. He spreads $\frac{1}{16}$ of the butter on his bread. Then he divides the rest of the butter into $\frac{3}{4}$ -pint containers. How many $\frac{3}{4}$ -pint containers is he able to fill? ______ $\frac{□}{□}$ containers

Answer: 1$\frac{1}{4}$ containers

Explanation: Alex opens a 1-pint container of orange butter. He spreads $\frac{1}{16}$ of the butter on his bread. 1 – 1/16 = 15/16 Then he divides the rest of the butter into $\frac{3}{4}$ -pint containers. (15/16) ÷ (3/4) = 5/4 = 1 1/4

Question 4. Kaitlin buys $\frac{9}{10}$ a pound of orange slices. She eats $\frac{1}{3}$ of them and divides the rest equally into 3 bags. How much is in each bag? ______ lb

Answer: 17/90 lb

Explanation: Kaitlin buys $\frac{9}{10}$ a pound of orange slices. She eats $\frac{1}{3}$ of them and divides the rest equally into 3 bags. If she starts with 9/10 pounds and has eaten 1/3 of them, 9/10 – 1/3 = 17/30 This is the amount she has left. Let’s divide this value by 3 to see how many pounds are in one bag. (17/30)/3 = 17/90 There are 17/90 pounds in one bag.

Question 5. Explain how to draw a model that represents $\left(1 \frac{1}{4}-\frac{1}{2}\right) \div \frac{1}{8}$. Type below: __________

Answer: Divide 2 bars into 8 quarters. Below that draw 1 1/4 or 5 quarters. Remove 1/2 or 2 quarters Divide each of the 3 quarters left into 2 eighths

Explanation: $\left(1 \frac{1}{4}-\frac{1}{2}\right) \div \frac{1}{8}$ 1 1/4 -1/2 = 5/4 – 1/2 = 3/4 3/4 ÷ 1/8 = 6

Lesson Check – Page No. 130

Question 1. Eva wanted to fill bags with $\frac{3}{4}$ pounds of trail mix. She started with 11 $\frac{3}{8}$ pounds but ate $\frac{1}{8}$ pound before she started filling the bags. How many bags could she fill? ______ bags

Answer: 15 bags

Explanation: 11 and 3/8-1/8=11 and 2/8=11 and 1/4 3/4 times x bags=11 and 1/4 convert 11 and 1/4 to improper fraction 11 and 1/4 = 11 + 1/4 = 44/4 + 1/4 = 45/4 3/4 times x bags=45/4 x bags = 45/4 × 4/3 = 15 bags she could fill 15 bags

Question 2. John has a roll containing 24 $\frac{2}{3}$ feet of wrapping paper. He wants to divide it into 11 pieces. First, though, he must cut off $\frac{5}{6}$ foot because it was torn. How long will each piece be? ______ $\frac{□}{□}$ feet

Answer: 2$\frac{4}{25}$ feet

Explanation: John had a roll containing wrapping paper = 24 2/3 = 74/3 First, he must cut off 5/6 foot because it was torn. He wants to divide it into 11 pieces. 74/3 – 5/6 Taking the L.C.M of 3 and 6 is 6 (148-5)/6 = 143/6 = 23.83 feet He wants to divide it into 11 pieces. length of the each piece = 23.83/11 = 2.16 feet

Question 3. Alexis has 32 $\frac{2}{5}$ ounces of beads. How many necklaces can she make if each uses 2 $\frac{7}{10}$ ounces of beads? ______ necklaces

Answer: 12 necklaces

Explanation: Alexis has 32 $\frac{2}{5}$ ounces of beads. If each uses 2 $\frac{7}{10}$ ounces of beads, 32 $\frac{2}{5}$ × 2 $\frac{7}{10}$ 32 $\frac{2}{5}$ = 162/5 2 $\frac{7}{10}$ = 27/10 162/5 × 27/10 = 12 necklaces

Question 4. Joseph has $32.40. He wants to buy several comic books that each cost $2.70. How many comic books can he buy? ______ comic books

Answer: 12 comic books

Explanation: Joseph has $32.40. He wants to buy several comic books that each cost $2.70. $32.40/$2.70 = 12 comic books

Question 5. A rectangle is 2 $\frac{4}{5}$ meters wide and 3 $\frac{1}{2}$ meters long. What is its area? ______ $\frac{□}{□}$ m 2

Answer: 9$\frac{4}{5}$ m2

Explanation: 2 $\frac{4}{5}$ = 14/5 3 $\frac{1}{2}$ = 7/2 14/5 × 7/2 = 9 4/5

Question 6. A rectangle is 2.8 meters wide and 3.5 meters long. What is its area? ______ m 2

Answer: 9.8 m 2

Explanation: A rectangle is 2.8 meters wide and 3.5 meters long. 2.8 × 3.5 = 9.8

Chapter 2 Review/Test – Page No. 131

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 24$

Answer: 0.45, 0.5, 5/8, 3/4

Explanation: 3/4 = 0.75 5/8 = 0.625 0.45, 0.5 0.45 < 0.5 < 0.625 < 0.75

Question 2. For numbers 2a–2d, compare. Choose <, >, or =. 2a. 0.75 _____ $\frac{3}{4}$ 2b. $\frac{4}{5}$ _____ 0.325 2c. 1 $\frac{3}{5}$ _____ 1.9 2d. 7.4 _____ 7 $\frac{2}{5}$

Answer: 2a. 0.75 = $\frac{3}{4}$ 2b. $\frac{4}{5}$ > 0.325 2c. 1 $\frac{3}{5}$ < 1.9 2d. 7.4 = 7 $\frac{2}{5}$

Explanation: 2a. 3/4 = 0.75 0.75 = 0.75 2b. $\frac{4}{5}$ = 0.8 0.8 > 0.325 2c. 1 $\frac{3}{5}$ = 8/5 = 1.6 1.6 < 1.9 2d. 7 $\frac{2}{5}$ = 37/5 = 7.4 7.4 = 7.4

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 25$

Answer: 3a. The oak tree is the shortest. True 3b. The birch tree is the tallest. False 3c. Two of the trees are the same height. False 3d. The sycamore tree is taller than the maple tree. False

Explanation: Sycamore = 15 2/3 = 47/3 = 15.666 Oak = 14 3/4 = 59/4 = 14.75 Maple = 15 3/4 = 63/4 = 15.75 Birch = 15.72

Page No. 132

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 26$

Answer: 4a. Point A represents 1.0. Yes 4b. Point B represents $\frac{3}{10}$. Yes 4c. Point C represents 6.5. No 4d. Point D represents $\frac{4}{5}$. Yes

Question 5. Select the values that are equivalent to one twenty-fifth. Mark all that apply. Options: a. 125 b. 25 c. 0.04 d. 0.025

Answer: c. 0.04

Explanation: one twenty-fifth = 1/25 = 0.04

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 27$

Answer: a. Simplified Expression: 1/10 Product: 0.1 b. Simplified Expression: 1/2 Product: 0.5 c. Simplified Expression: 15/56 Product: 0.267 d. Simplified Expression: 1/12 Product: 0.083

Explanation: a. 2/5 × 1/4 = 2/20 Simplify using the GCF. The GCF of 2 and 20 is 2. Divide the numerator and the denominator by 2. So, 1/10 is the answer. Product: 0.1 b. 4/5 × 5/8 = 1/2 Product: 0.5 c. 3/7 × 5/8 = 15/ 56 Product: 0.267 d. 4/9 × 3/16 = 1/12 Product: 0.083

Page No. 133

Question 7. Two-fifths of the fish in Gary’s fish tank are guppies. One fourth of the guppies are red. What fraction of the fish in Gary’s tank are red guppies? What fraction of the fish in Gary’s tank are not red guppies? Show your work. Type below: ___________

Answer: 1/10 of the fish are red guppies. and 9/10 of the fish are not red guppies.

Explanation: two-fifths of the fish in Gary’s fish tank are guppies. One-fourth of the guppies are red. Let the total number of fish in Gary’s fish tank be x. It is given that two-fifths of the fish in Gary’s fish tank are guppies. So, the number of guppies in Gary’s fish tank is 2/5 × x Given that One-fourth of the guppies are red. number of red guppies = 1/4 × 2x/5 = x/10 So, 1/10 of the fish are red guppies. 1 – 1/10 = 9/10 of the fish are not red guppies.

Question 8. One-third of the students at Finley High School play sports. Two-fifths of the students who play sports are girls. What fraction of all students are girls who play sports? Use numbers and words to explain your answer. Type below: ___________

Answer: One-third of the students at Finley High School play sports. Two-fifths of the students who play sports are girls. 1/3 × 2/5 = 2/15 of the girls in the school play sports.

Question 9. Draw a model to find the quotient. $\frac{3}{4}$ ÷ 2 = $\frac{3}{4}$ ÷ $\frac{3}{8}$ = How are your models alike? How are they different? Type below: ___________

Explanation: $\frac{3}{4}$ ÷ 2 = 3/4 × 1/2 = 3/8 $\frac{3}{4}$ ÷ $\frac{3}{8}$ = 3/4 × 8/3 = 2 Both models are multiplying with the 3/4. The number line model shows how many groups of 3/8 are in 3/4.

Question 10. Explain how to use a model to find the quotient. 2 $\frac{1}{2}$ ÷ 2 = Type below: ___________

Answer: 5/4

Explanation: 2 1/2 = 5/2 5/2 groups of 2 5/2 ÷ 2 = 5/2 × 1/2 = 5/4

Page No. 134

Divide. Show your work.

Question 11. $\frac{7}{8}$ ÷ $\frac{3}{5}$ = _______ $\frac{□}{□}$

Answer: 1 $\frac{11}{24}$

Explanation: $\frac{7}{8}$ ÷ $\frac{3}{5}$ $\frac{7}{8}$ × $\frac{5}{3}$ = 35/24 = 1 $\frac{11}{24}$

Question 12. $2 \frac{1}{10} \div 1 \frac{1}{5}=$ = _______ $\frac{□}{□}$

Answer: 1 $\frac{3}{4}$

Explanation: 2 $\frac{1}{10}$ = 21/10 1 $\frac{1}{5}$ = 6/5 (21/10) ÷ (6/5) = 7/4 or 1 3/4

Question 13. Sophie has $\frac{3}{4}$ quart of lemonade. If she divides the lemonade into glasses that hold $\frac{1}{16}$ quart, how many glasses can Sophie fill? Show your work _______ glasses

Answer: 12 glasses

Explanation: Let x be the number of glasses 1/16x = 3/4 x = 3/4 × 16 = 3 × 4 = 12 glasses

Question 14. Ink cartridges weigh $\frac{1}{8}$ pound. The total weight of the cartridges in a box is 4 $\frac{1}{2}$ pounds. How many cartridges does the box contain? Show your work and explain why you chose the operation you did. _______ cartridges

Answer: 36 cartridges

Explanation: Weight of ink cartridges = 1/8 pounds Total weight of the cartridges in a box = 4 1/2 = 9/2 pounds so, the Number of cartridges that box contain is given by 9/2 ÷ 1/8 = 36 Hence, there are 36 cartridges that box contain.

Question 15. Beth had 1 yard of ribbon. She used $\frac{1}{3}$ yard for a project. She wants to divide the rest of the ribbon into pieces $\frac{1}{6}$ yard long. How many $\frac{1}{6}$ yard pieces of ribbon can she make? Explain your solution. _______ pieces

Answer: 4 pieces

Explanation: Beth had 1 yard of ribbon. She used $\frac{1}{3}$ yard for a project. 1 – $\frac{1}{3}$ = 2/3 yard left She wants to divide the rest of the ribbon into pieces $\frac{1}{6}$ yard long. 2/3 ÷ 1/6 = 4

Page No. 135

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 28$

Answer: 1/5 ÷ 3/4 = 4/15; 1/5 × 4/3 = 4/15 2/13 ÷ 1/5 = 10/13; 2/13 × 5/1 = 10/13 4/5 ÷ 3/5 = 4/3; 4/5 × 5/3 = 4/3 the product of the each pair of division and multiplication problems are the same. They are different from the operation performed.

Question 16. Part B Explain how to use the pattern in the table to rewrite a division problem involving fractions as a multiplication problem. Type below: ___________

Answer: First, since it’s the division you have to change the second fraction which is called the reciprocal. That means the second fraction has to be flipped before you can multiple the fractions.

Page No. 136

$Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 29$

Answer: Margie hiked a 17 7/8 mile trail. Distance hiked by Margie = 17 7/8 = 143/8 mile. She stopped every 3 2/5 miles to take a picture = 17/5 mile Number of pictures = (143/8) ÷ (17/5) = 715/136 = 5.28 So she can take a maximum of 6 pictures and a minimum of 5 pictures. B is the correct answer.

Question 18. Brad and Wes are building a tree house. They cut a 12 $\frac{1}{2}$ foot piece of wood into 5 of the same length pieces. How long is each piece of wood? Show your work. _______ $\frac{□}{□}$ foot

Answer: 2 $\frac{1}{2}$ foot

Explanation: Brad and Wes cut a 12 1/2foot piece of wood into 5 of the same length. Let the length of 1 piece be x So, Length of 5 pieces = 5x The total length of wood = 25/2 5x = 25/2 x = 5/2 = 2 1/2

Free Grade 6 HMH Go Math Answer Key PDF Download

In addition, to the exercise problems students of grade 6 can get the solutions for mid-chapter checkpoint and review test also. So, start solving the problems which are at the end of the chapter and check the solutions from here. Hope the information regarding Go Math 6th Grade Answer Key Chapter 2 Fractions and Decimals is helpful for you to overcome the issues in maths. Check out the links and start solving all the questions.

Go Math! 4 Common Core, Grade: 4 Publisher: Houghton Mifflin Harcourt

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Solving multiplication and division problems using the bar model

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In this lesson, we will learn how to use the bar model when solving multiplication and division problems. We will analyse word problems to select the most important part of the text and determine the maths required, then translate this into a suitable bar model to help us solve the problem.

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Starter quiz

5 questions, lesson appears in, unit maths / deriving multiplication and division facts.

COMMENTS

Problem Solving
This lesson shows how to "Act It Out" to model division. Easy lesson. :)
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Go Math! 4 Common Core answers & resources
Use the table below to find videos, mobile apps, worksheets and lessons that supplement Go Math! 4 Common Core.
Solving multiplication and division problems using the bar model
In this lesson, we will learn how to use the bar model when solving multiplication and division problems. We will analyse word problems to select the most important part of the text and determine the maths required, then translate this into a suitable bar model to help us solve the problem.
PDF Grade 6
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These activities for chapter 6 lesson 1 are designed to help your students master the concept of problem solving/model division. This is a great resource to accompany your 3rd grade Go Math curriculum! The interactive practice slides are easy to manipulate and provide intriguing methods to help stu...