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5th grade (Eureka Math/EngageNY)

Unit 1: module 1: place value and decimal fractions, unit 2: module 2: multi-digit whole number and decimal fraction operations, unit 3: module 3: addition and subtractions of fractions, unit 4: module 4: multiplication and division of fractions and decimal fractions, unit 5: module 5: addition and multiplication with volume and area, unit 6: module 6: problem solving with the coordinate plane.

eureka grade 5 module 1 lesson 13 homework

Engage NY // Eureka Math Grade 5 Module 1 Lesson 13 Homework

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Eureka Math Grade 5 Module 4 Lesson 13 Answer Key

Engage ny eureka math 5th grade module 4 lesson 13 answer key, eureka math grade 5 module 4 lesson 13 problem set answer key.

Solve. Draw a rectangular fraction model to show your thinking. Then, write a multiplication sentence. The first one has been done for you.

Eureka Math Grade 5 Module 4 Lesson 13 Problem Set Answer Key 1

b. Half of \(\frac{1}{3}\) pan of brownies = _____ pan of brownies.

Answer: \(\frac{1}{6}\) pan of brownies.

Explanation: Given that there is half of \(\frac{1}{3}\) pan of brownies which is \(\frac{1}{2}\) × \(\frac{1}{3}\) = \(\frac{1}{6}\) pan of brownies.

c. A fourth of \(\frac{1}{3}\) pan of brownies = _____ pan of brownies.

Answer: \(\frac{1}{12}\) pan of brownies.

Explanation: Given that there is half of \(\frac{1}{3}\) pan of brownies which is \(\frac{1}{4}\) × \(\frac{1}{3}\) = \(\frac{1}{12}\) pan of brownies.

d. \(\frac{1}{4}\) of \(\frac{1}{4}\)

Answer: \(\frac{1}{16}\).

Explanation: Given that \(\frac{1}{4}\) of \(\frac{1}{4}\) which is \(\frac{1}{4}\) × \(\frac{1}{4}\) = \(\frac{1}{16}\).

e. \(\frac{1}{2}\) of \(\frac{1}{6}\)

Answer: \(\frac{1}{12}\).

Explanation: Given that \(\frac{1}{2}\) of \(\frac{1}{6}\) which is \(\frac{1}{2}\) × \(\frac{1}{6}\) = \(\frac{1}{12}\).

Question 2. Draw rectangular fraction models of 3 × \(\frac{1}{4}\) and \(\frac{1}{3}\) × \(\frac{1}{4}\). Compare multiplying a number by 3 and by 1 third.

Answer: \(\frac{3}{4}\) > \(\frac{1}{12}\).

Eureka-Math-Grade-5-Module-4-Lesson-13-Problem-Set-Answer-Key-1-1

Question 3. \(\frac{1}{2}\) of Ila’s workspace is covered in paper. \(\frac{1}{3}\) of the paper is covered in yellow sticky notes. What fraction of Ila’s workspace is covered in yellow sticky notes? Draw a picture to support your answer.

Answer: \(\frac{1}{6}\)

Explanation: Given that \(\frac{1}{2}\) of Ila’s workspace is covered in paper and \(\frac{1}{3}\) of the paper is covered in yellow sticky notes, so the fraction of Ila’s workspace is covered in yellow sticky notes is \(\frac{1}{2}\) × \(\frac{1}{3}\) which is \(\frac{1}{6}\).

Question 4. A marching band is rehearsing in rectangular formation. \(\frac{1}{5}\) of the marching band members play percussion instruments. \(\frac{1}{2}\) of the percussionists play the snare drum. What fraction of all the band members play the snare drum?

Answer: The fraction of all the band members who play the snare drum is \(\frac{1}{10}\).

Explanation: Given that a \(\frac{1}{5}\) of the marching band members play percussion instruments and \(\frac{1}{2}\) of the percussionists play the snare drum, so the fraction of all the band members play the snare drum is \(\frac{1}{2}\) of \(\frac{1}{5}\) which is \(\frac{1}{2}\) × \(\frac{1}{5}\) = \(\frac{1}{10}\).

Question 5. Marie is designing a bedspread for her grandson’s new bedroom. \(\frac{2}{3}\) of the bedspread is covered in race cars, and the rest is striped. \(\frac{1}{4}\) of the stripes are red. What fraction of the bedspread is covered in red stripes?

Answer: The fraction of the bedspread is covered in red stripes is \(\frac{1}{12}\).

Explanation: Given that \(\frac{2}{3}\) of the bedspread is covered in race cars, and the rest is stripped and \(\frac{1}{4}\) of the stripes are red. The striped bedspread would be 1 – \(\frac{2}{3}\) which is \(\frac{1}{3}\). So the fraction of the bedspread is covered in red stripes is \(\frac{1}{3}\) × \(\frac{1}{4}\) which is \(\frac{1}{12}\).

Eureka Math Grade 5 Module 4 Lesson 13 Exit Ticket Answer Key

Question 1. Solve. Draw a rectangular fraction model, and write a number sentence to show your thinking.

\(\frac{1}{3}\) × \(\frac{1}{3}\) =

Answer: \(\frac{1}{9}\).

Explanation: Given that \(\frac{1}{3}\) × \(\frac{1}{3}\) which is \(\frac{1}{9}\).

Question 2. Ms. Sheppard cuts \(\frac{1}{2}\) of a piece of construction paper. She uses \(\frac{1}{6}\) of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?

Answer: The fraction of the sheet of paper does she use to make the flower is \(\frac{1}{12}\).

Explanation: Given that Ms. Sheppard cuts \(\frac{1}{2}\) of a piece of construction paper and she uses \(\frac{1}{6}\) of the piece to make a flower, so the fraction of the sheet of paper does she use to make the flower is \(\frac{1}{2}\) × \(\frac{1}{6}\) which is \(\frac{1}{12}\).

Eureka Math Grade 5 Module 4 Lesson 13 Homework Answer Key

Solve. Draw a rectangular fraction model to show your thinking.

a. Half of \(\frac{1}{2}\) cake = _____ cake.

Answer: \(\frac{1}{4}\).

Explanation: Given that half of \(\frac{1}{2}\) cake which is \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{4}\).

b. One-third of \(\frac{1}{2}\) cake = _____ cake.

Answer: \(\frac{1}{6}\).

Explanation: Given that One-third of \(\frac{1}{2}\) cake which is \(\frac{1}{3}\) × \(\frac{1}{2}\) = \(\frac{1}{6}\).

c. \(\frac{1}{4}\) of \(\frac{1}{2}\)

Answer: \(\frac{1}{8}\).

Explanation: Given that latex]\frac{1}{4}[/latex] of \(\frac{1}{2}\) which is latex]\frac{1}{4}[/latex] × \(\frac{1}{2}\) = \(\frac{1}{8}\).

d. \(\frac{1}{2}\) × \(\frac{1}{5}\)

Answer: \(\frac{1}{10}\).

Explanation: Given that latex]\frac{1}{2}[/latex] of \(\frac{1}{5}\) which is latex]\frac{1}{2}[/latex] × \(\frac{1}{5}\) = \(\frac{1}{10}\).

e. \(\frac{1}{3}\) × \(\frac{1}{3}\)

Explanation: Given that latex]\frac{1}{3}[/latex] of \(\frac{1}{3}\) which is latex]\frac{1}{3}[/latex] × \(\frac{1}{3}\) = \(\frac{1}{9}\).

f. \(\frac{1}{4}\) × \(\frac{1}{3}\)

Explanation: Given that latex]\frac{1}{4}[/latex] of \(\frac{1}{3}\) which is latex]\frac{1}{4}[/latex] × \(\frac{1}{3}\) = \(\frac{1}{12}\).

Question 2. Noah mows \(\frac{1}{2}\) of his property and leaves the rest wild. He decides to use \(\frac{1}{5}\) of the wild area for a vegetable garden. What fraction of the property is used for the garden? Draw a picture to support your answer.

Answer: The fraction of the property is used for the garden is \(\frac{1}{10}\).

Explanation: Given that Noah mows \(\frac{1}{2}\) of his property and leaves the rest wild and he decides to use \(\frac{1}{5}\) of the wild area for a vegetable garden, so the fraction of the property is used for the garden is \(\frac{1}{2}\) × \(\frac{1}{5}\) which is \(\frac{1}{2}\) × \(\frac{1}{5}\) = \(\frac{1}{10}\).

Question 3. Fawn plants \(\frac{2}{3}\) of the garden with vegetables. Her son plants the remainder of the garden. He decides to use \(\frac{1}{2}\) of his space to plant flowers, and in the rest, he plants herbs. What fraction of the entire garden is planted in flowers? Draw a picture to support your answer.

Answer: The fraction of the entire garden is planted in flowers is \(\frac{1}{6}\).

Explanation: Given that fawn plants \(\frac{2}{3}\) of the garden with vegetables and her son plants the remainder of the garden and he decides to use \(\frac{1}{2}\) of his space to plant flowers, and in the rest, he plants herbs. So her son gets \(\frac{2}{3}\) × \(\frac{1}{2}\) which is \(\frac{1}{3}\). So the fraction of the entire garden is planted in flowers is \(\frac{1}{2}\) × \(\frac{1}{3}\) which is \(\frac{1}{6}\).

Question 4. Diego eats \(\frac{1}{5}\) of a loaf of bread each day. On Tuesday, Diego eats \(\frac{1}{4}\) of the day’s portion before lunch. What fraction of the whole loaf does Diego eat before lunch on Tuesday? Draw a rectangular fraction model to support your thinking.

Answer: The fraction of the whole loaf does Diego eat before lunch on Tuesday is \(\frac{1}{20}\).

Explanation: Given that Diego eats \(\frac{1}{5}\) of a loaf of bread each day and on tuesday, Diego eats \(\frac{1}{4}\) of the day’s portion before lunch. So the fraction of the whole loaf does Diego eat before lunch on Tuesday is \(\frac{1}{5}\) × \(\frac{1}{4}\) which is \(\frac{1}{20}\).

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