fractions and decimals homework 2

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Key to Fractions Workbooks

These workbooks by Key Curriculum Press feature a number of exercises to help your child learn about fractions. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Each book has a practice test at the end.

Decimals Worksheets

Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.

Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions.

Most Popular Decimals Worksheets this Week

Grids and Charts Useful for Learning Decimals

General use decimal printables are used in a variety of contexts and assist students in completing math questions related to decimals.

The thousandths grid is a useful tool in representing decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.

• Thousandths and Hundredths Grids Thousandths Grid Hundredths Grids ( 4 on a page) Hundredths Grids ( 9 on a page) Hundredths Grids ( 20 on a page)
• Decimal Place Value Charts Decimal Place Value Chart ( Ones to Hundredths ) Decimal Place Value Chart ( Ones to Thousandths ) Decimal Place Value Chart ( Hundreds to Hundredths ) Decimal Place Value Chart ( Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Millions to Millionths )

Decimals in Expanded Form

For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart, and allow them to use it when converting standard form numbers to expanded form. There are actually five ways (two more than with integers) to write expanded form for decimals, and which one you use depends on your application or preference. Here is a quick summary of the various ways using the decimal number 1.23. 1. Expanded Form using decimals: 1 + 0.2 + 0.03 2. Expanded Form using fractions: 1 + 2 ⁄ 10 + 3 ⁄ 100 3. Expanded Factors Form using decimals: (1 × 1) + (2 × 0.1) + (3 × 0.01) 4. Expanded Factors Form using fractions: (1 × 1) + (2 × 1 ⁄ 10 ) + (3 × 1 ⁄ 100 ) 5. Expanded Exponential Form: (1 × 10 0 ) + (2 × 10 -1 ) + (3 × 10 -2 )

• Converting Decimals from Standard Form to Expanded Form Using Decimals Converting Decimals from Standard to Expanded Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Form Using Fractions Converting Decimals from Standard to Expanded Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Factors Form Using Decimals Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Factors Form Using Fractions Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Exponential Form Converting Decimals from Standard to Expanded Exponential Form ( 3 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 4 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 5 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 6 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 7 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 8 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 9 Decimal Places)
• Retro Converting Decimals from Standard Form to Expanded Form Retro Standard to Expanded Form (3 digits before decimal; 2 after) Retro Standard to Expanded Form (4 digits before decimal; 3 after) Retro Standard to Expanded Form (6 digits before decimal; 4 after) Retro Standard to Expanded Form (12 digits before decimal; 3 after)
• Retro European Format Converting Decimals from Standard Form to Expanded Form Standard to Expanded Form (3 digits before decimal; 2 after) Standard to Expanded Form (4 digits before decimal; 3 after) Standard to Expanded Form (6 digits before decimal; 4 after)

Of course, being able to convert numbers already in expanded form to standard form is also important. All five versions of decimal expanded form are included in these worksheets.

• Converting Decimals to Standard Form from Expanded Form Using Decimals Converting Decimals from Expanded Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Form Using Fractions Converting Decimals from Expanded Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Factors Form Using Decimals Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Factors Form Using Fractions Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Exponential Form Converting Decimals from Expanded Exponential Form to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 9 Decimal Places)
• Retro Converting Decimals to Standard Form from Expanded Form Retro Expanded to Standard Form (3 digits before decimal; 2 after) Retro Expanded to Standard Form (4 digits before decimal; 3 after) Retro Expanded to Standard Form (6 digits before decimal; 4 after) Retro Expanded to Standard Form (12 digits before decimal; 3 after)
• Retro European Format Converting Decimals to Standard Form from Expanded Form Retro European Format Expanded to Standard Form (3 digits before decimal; 2 after) Retro European Format Expanded to Standard Form (4 digits before decimal; 3 after) Retro European Format Expanded to Standard Form (6 digits before decimal; 4 after)

Rounding Decimals Worksheets

Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4.567 to the nearest tenth. First, truncate the number after the tenths place 4.5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4.6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6.959 to the nearest tenth. Truncate: 6.9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7.0. Watch that students do not write 6.10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...

We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6.5 --> 7; 3.555 --> 3.56; 0.60500 --> 0.61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5.5 would be rounded up to 6, but 8.5 would be rounded down to 8. The main reason for this is not to skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most pre-college students round up on a 5, that is what we have done in the worksheets that follow.

• Rounding Decimals to Whole Numbers Round Tenths to a Whole Number Round Hundredths to a Whole Number Round Thousandths to a Whole Number Round Ten Thousandths to a Whole Number Round Various Decimals to a Whole Number
• Rounding Decimals to Tenths Round Hundredths to Tenths Round Thousandths to Tenths Round Ten Thousandths to Tenths Round Various Decimals to Tenths
• Rounding Decimals to Hundredths Round Thousandths to Hundredths Round Ten Thousandths to Hundredths Round Various Decimals to Hundredths
• Rounding Decimals to Thousandths Round Ten Thousandths to Thousandths
• Rounding Decimals to Various Decimal Places Round Hundredths to Various Decimal Places Round Thousandths to Various Decimal Places Round Ten Thousandths to Various Decimal Places Round Various Decimals to Various Decimal Places
• European Format Rounding Decimals to Whole Numbers European Format Round Tenths to a Whole Number European Format Round Hundredths to a Whole Number European Format Round Thousandths to a Whole Number European Format Round Ten Thousandths to Whole Number
• European Format Rounding Decimals to Tenths European Format Round Hundredths to Tenths European Format Round Thousandths to Tenths European Format Round Ten Thousandths to Tenths
• European Format Rounding Decimals to Hundredths European Format Round Thousandths to Hundredths European Format Round Ten Thousandths to Hundredths
• European Format Rounding Decimals to Thousandths European Format Round Ten Thousandths to Thousandths

Comparing and Ordering/Sorting Decimals Worksheets.

The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.

Students who have mastered comparing whole numbers should find comparing decimals to be fairly easy. The easiest strategy is to compare the numbers before the decimal (the whole number part) first and only compare the decimal parts if the whole number parts are equal. These sorts of questions allow teachers/parents to get a good idea of whether students have grasped the concept of decimals or not. For example, if a student thinks that 4.93 is greater than 8.7, then they might need a little more instruction in place value. Close numbers means that some care was taken to make the numbers look similar. For example, they could be close in value, e.g. 3.3. and 3.4 or one of the digits might be changed as in 5.86 and 6.86.

• Comparing Decimals up to Tenths Comparing Decimals up to Tenths ( Both Numbers Random ) Comparing Decimals up to Tenths ( One Digit Differs ) Comparing Decimals up to Tenths ( Both Numbers Close in Value ) Comparing Decimals up to Tenths ( Various Tricks )
• Comparing Decimals up to Hundredths Comparing Decimals up to Hundredths ( Both Numbers Random ) Comparing Decimals up to Hundredths ( One Digit Differs ) Comparing Decimals up to Hundredths ( Two Digits Swapped ) Comparing Decimals up to Hundredths ( Both Numbers Close in Value ) Comparing Decimals up to Hundredths ( One Number has an Extra Digit ) Comparing Decimals up to Hundredths ( Various Tricks )
• Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths ( One Digit Differs ) Comparing Decimals up to Thousandths ( Two Digits Swapped ) Comparing Decimals up to Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Thousandths ( Various Tricks )
• Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths ( One Digit Differs ) Comparing Decimals up to Ten Thousandths ( Two Digits Swapped ) Comparing Decimals up to Ten Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Ten Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Ten Thousandths ( Various Tricks )
• Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths ( One Digit Differs ) Comparing Decimals up to Hundred Thousandths ( Two Digits Swapped ) Comparing Decimals up to Hundred Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Hundred Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Hundred Thousandths ( Various Tricks )
• European Format Comparing Decimals European Format Comparing Decimals up to Tenths European Format Comparing Decimals up to Tenths (tight) European Format Comparing Decimals up to Hundredths European Format Comparing Decimals up to Hundredths (tight) European Format Comparing Decimals up to Thousandths European Format Comparing Decimals up to Thousandths (tight)

Ordering decimals is very much like comparing decimals except there are more than two numbers. Generally, students determine the least (or greatest) decimal to start, cross it off the list then repeat the process to find the next lowest/greatest until they get to the last number. Checking the list at the end is always a good idea.

• Ordering/Sorting Decimals Ordering/Sorting Decimal Hundredths Ordering/Sorting Decimal Thousandths
• European Format Ordering/Sorting Decimals European Format Ordering/Sorting Decimal Tenths (8 per set) European Format Ordering/Sorting Decimal Hundredths (8 per set) European Format Ordering/Sorting Decimal Thousandths (8 per set) European Format Ordering/Sorting Decimal Ten Thousandths (8 per set) European Format Ordering/Sorting Decimals with Various Decimal Places(8 per set)

Converting Decimals to Fractions and Other Number Formats

There are many good reasons for converting decimals to other number formats. Dealing with a fraction in arithmetic is often easier than the equivalent decimal. Consider 0.333... which is equivalent to 1/3. Multiplying 300 by 0.333... is difficult, but multiplying 300 by 1/3 is super easy! Students should be familiar with some of the more common fraction/decimal conversions, so they can switch back and forth as needed.

• Converting Between Decimals and Fractions Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
• Converting Between Decimals, Fraction, Percents and Ratios Converting Fractions to Decimals, Percents and Part-to-Part Ratios Converting Fractions to Decimals, Percents and Part-to-Whole Ratios Converting Decimals to Fractions, Percents and Part-to-Part Ratios Converting Decimals to Fractions, Percents and Part-to-Whole Ratios Converting Percents to Fractions, Decimals and Part-to-Part Ratios Converting Percents to Fractions, Decimals and Part-to-Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios with 7ths and 11ths

Adding and Subtracting Decimals

Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3.25 + 4.98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3.25 + 4.98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8.23)

• Adding Tenths Adding Decimal Tenths with 0 Before the Decimal (range 0.1 to 0.9) Adding Decimal Tenths with 1 Digit Before the Decimal (range 1.1 to 9.9) Adding Decimal Tenths with 2 Digits Before the Decimal (range 10.1 to 99.9)
• Adding Hundredths Adding Decimal Hundredths with 0 Before the Decimal (range 0.01 to 0.99) Adding Decimal Hundredths with 1 Digit Before the Decimal (range 1.01 to 9.99) Adding Decimal Hundredths with 2 Digits Before the Decimal (range 10.01 to 99.99)
• Adding Thousandths Adding Decimal Thousandths with 0 Before the Decimal (range 0.001 to 0.999) Adding Decimal Thousandths with 1 Digit Before the Decimal (range 1.001 to 9.999) Adding Decimal Thousandths with 2 Digits Before the Decimal (range 10.001 to 99.999)
• Adding Ten Thousandths Adding Decimal Ten Thousandths with 0 Before the Decimal (range 0.0001 to 0.9999) Adding Decimal Ten Thousandths with 1 Digit Before the Decimal (range 1.0001 to 9.9999) Adding Decimal Ten Thousandths with 2 Digits Before the Decimal (range 10.0001 to 99.9999)
• Adding Various Decimal Places Adding Various Decimal Places with 0 Before the Decimal Adding Various Decimal Places with 1 Digit Before the Decimal Adding Various Decimal Places with 2 Digits Before the Decimal Adding Various Decimal Places with Various Numbers of Digits Before the Decimal
• European Format Adding Decimals European Format Adding decimal tenths with 0 before the decimal (range 0,1 to 0,9) European Format Adding decimal tenths with 1 digit before the decimal (range 1,1 to 9,9) European Format Adding decimal hundredths with 0 before the decimal (range 0,01 to 0,99) European Format Adding decimal hundredths with 1 digit before the decimal (range 1,01 to 9,99) European Format Adding decimal thousandths with 0 before the decimal (range 0,001 to 0,999) European Format Adding decimal thousandths with 1 digit before the decimal (range 1,001 to 9,999) European Format Adding decimal ten thousandths with 0 before the decimal (range 0,0001 to 0,9999) European Format Adding decimal ten thousandths with 1 digit before the decimal (range 1,0001 to 9,9999) European Format Adding mixed decimals with Various Decimal Places European Format Adding mixed decimals with Various Decimal Places (1 to 9 before decimal)

Base ten blocks can be used for decimal subtraction. Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.

• Subtracting Tenths Subtracting Decimal Tenths with No Integer Part Subtracting Decimal Tenths with an Integer Part in the Minuend Subtracting Decimal Tenths with an Integer Part in the Minuend and Subtrahend
• Subtracting Hundredths Subtracting Decimal Hundredths with No Integer Part Subtracting Decimal Hundredths with an Integer Part in the Minuend and Subtrahend Subtracting Decimal Hundredths with a Larger Integer Part in the Minuend
• Subtracting Thousandths Subtracting Decimal Thousandths with No Integer Part Subtracting Decimal Thousandths with an Integer Part in the Minuend and Subtrahend
• Subtracting Ten Thousandths Subtracting Decimal Ten Thousandths with No Integer Part Subtracting Decimal Ten Thousandths with an Integer Part in the Minuend and Subtrahend
• Subtracting Various Decimal Places Subtracting Various Decimals to Hundredths Subtracting Various Decimals to Thousandths Subtracting Various Decimals to Ten Thousandths
• European Format Subtracting Decimals European Format Decimal subtraction (range 0,1 to 0,9) European Format Decimal subtraction (range 1,1 to 9,9) European Format Decimal subtraction (range 0,01 to 0,99) European Format Decimal subtraction (range 1,01 to 9,99) European Format Decimal subtraction (range 0,001 to 0,999) European Format Decimal subtraction (range 1,001 to 9,999) European Format Decimal subtraction (range 0,0001 to 0,9999) European Format Decimal subtraction (range 1,0001 to 9,9999) European Format Decimal subtraction with Various Decimal Places European Format Decimal subtraction with Various Decimal Places (1 to 9 before decimal)

Adding and subtracting decimals is fairly straightforward when all the decimals are lined up. With the questions arranged horizontally, students are challenged to understand place value as it relates to decimals. A wonderful strategy for placing the decimal is to use estimation. For example if the question is 49.2 + 20.1, the answer without the decimal is 693. Estimate by rounding 49.2 to 50 and 20.1 to 20. 50 + 20 = 70. The decimal in 693 must be placed between the 9 and the 3 as in 69.3 to make the number close to the estimate of 70.

The above strategy will go a long way in students understanding operations with decimals, but it is also important that they have a strong foundation in place value and a proficiency with efficient strategies to be completely successful with these questions. As with any math skill, it is not wise to present this to students until they have the necessary prerequisite skills and knowledge.

• Horizontally Arranged Adding Decimals Adding Decimals to Tenths Horizontally Adding Decimals to Hundredths Horizontally Adding Decimals to Thousandths Horizontally Adding Decimals to Ten Thousandths Horizontally Adding Decimals Horizontally With Up to Two Places Before and After the Decimal Adding Decimals Horizontally With Up to Three Places Before and After the Decimal Adding Decimals Horizontally With Up to Four Places Before and After the Decimal
• Horizontally Arranged Subtracting Decimals Subtracting Decimals to Tenths Horizontally Subtracting Decimals to Hundredths Horizontally Subtracting Decimals to Thousandths Horizontally Subtracting Decimals to Ten Thousandths Horizontally Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal
• Horizontally Arranged Mixed Adding and Subtracting Decimals Adding and Subtracting Decimals to Tenths Horizontally Adding and Subtracting Decimals to Hundredths Horizontally Adding and Subtracting Decimals to Thousandths Horizontally Adding and Subtracting Decimals to Ten Thousandths Horizontally Adding and Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal

Multiplying and Dividing Decimals

Multiplying decimals by whole numbers is very much like multiplying whole numbers except there is a decimal to deal with. Although students might initially have trouble with it, through the power of rounding and estimating, they can generally get it quite quickly. Many teachers will tell students to ignore the decimal and multiply the numbers just like they would whole numbers. This is a good strategy to use. Figuring out where the decimal goes at the end can be accomplished by counting how many decimal places were in the original question and giving the answer that many decimal places. To better understand this method, students can round the two factors and multiply in their head to get an estimate then place the decimal based on their estimate. For example, multiplying 9.84 × 91, students could first round the numbers to 10 and 91 (keep 91 since multiplying by 10 is easy) then get an estimate of 910. Actually multiplying (ignoring the decimal) gets you 89544. To get that number close to 910, the decimal needs to go between the 5 and the 4, thus 895.44. Note that there are two decimal places in the factors and two decimal places in the answer, but estimating made it more understandable rather than just a method.

• Multiplying Decimals by 1-Digit Whole Numbers Multiply 2-digit tenths by 1-digit whole numbers Multiply 2-digit hundredths by 1-digit whole numbers Multiply 2-digit thousandths by 1-digit whole numbers Multiply 3-digit tenths by 1-digit whole numbers Multiply 3-digit hundredths by 1-digit whole numbers Multiply 3-digit thousandths by 1-digit whole numbers Multiply various decimals by 1-digit whole numbers
• Multiplying Decimals by 2-Digit Whole Numbers Multiplying 2-digit tenths by 2-digit whole numbers Multiplying 2-digit hundredths by 2-digit whole numbers Multiplying 3-digit tenths by 2-digit whole numbers Multiplying 3-digit hundredths by 2-digit whole numbers Multiplying 3-digit thousandths by 2-digit whole numbers Multiplying various decimals by 2-digit whole numbers
• Multiplying Decimals by Tenths Multiplying 2-digit whole by 2-digit tenths Multiplying 2-digit tenths by 2-digit tenths Multiplying 2-digit hundredths by 2-digit tenths Multiplying 3-digit whole by 2-digit tenths Multiplying 3-digit tenths by 2-digit tenths Multiplying 3-digit hundredths by 2-digit tenths Multiplying 3-digit thousandths by 2-digit tenths Multiplying various decimals by 2-digit tenths
• Multiplying Decimals by Hundredths Multiplying 2-digit whole by 2-digit hundredths Multiplying 2-digit tenths by 2-digit hundredths Multiplying 2-digit hundredths by 2-digit hundredths Multiplying 3-digit whole by 2-digit hundredths Multiplying 3-digit tenths by 2-digit hundredths Multiplying 3-digit hundredths by 2-digit hundredths Multiplying 3-digit thousandths by 2-digit hundredths Multiplying various decimals by 2-digit hundredths
• Multiplying Decimals by Various Decimal Places Multiplying 2-digit by 2-digit numbers with various decimal places Multiplying 3-digit by 2-digit numbers with various decimal places
• Decimal Long Multiplication in Various Ranges Decimal Multiplication (range 0.1 to 0.9) Decimal Multiplication (range 1.1 to 9.9) Decimal Multiplication (range 10.1 to 99.9) Decimal Multiplication (range 0.01 to 0.99) Decimal Multiplication (range 1.01 to 9.99) Decimal Multiplication (range 10.01 to 99.99) Random # Digits Random # Places
• European Format Multiplying Decimals by 2-Digit Whole Numbers European Format 2-digit whole × 2-digit hundredths European Format 2-digit tenths × 2-digit whole European Format 2-digit hundredths × 2-digit whole European Format 3-digit tenths × 2-digit whole European Format 3-digit hundredths × 2-digit whole European Format 3-digit thousandths × 2-digit whole
• European Format Multiplying Decimals by 2-Digit Tenths European Format 2-digit whole × 2-digit tenths European Format 2-digit tenths × 2-digit tenths European Format 2-digit hundredths × 2-digit tenths European Format 3-digit whole × 2-digit tenths European Format 3-digit tenths × 2-digit tenths European Format 3-digit hundredths × 2-digit tenths European Format 3-digit thousandths × 2-digit tenths
• European Format Multiplying Decimals by 2-Digit Hundredths European Format 2-digit tenths × 2-digit hundredths European Format 2-digit hundredths × 2-digit hundredths European Format 3-digit whole × 2-digit hundredths European Format 3-digit tenths × 2-digit hundredths European Format 3-digit hundredths × 2-digit hundredths European Format 3-digit thousandths × 2-digit hundredths
• European Format Multiplying Decimals by Various Decimal Places European Format 2-digit × 2-digit with various decimal places European Format 3-digit × 2-digit with various decimal places
• Dividing Decimals by Whole Numbers Divide Tenths by a Whole Number Divide Hundredths by a Whole Number Divide Thousandths by a Whole Number Divide Ten Thousandths by a Whole Number Divide Various Decimals by a Whole Number

In case you aren't familiar with dividing with a decimal divisor, the general method for completing questions is by getting rid of the decimal in the divisor. This is done by multiplying the divisor and the dividend by the same amount, usually a power of ten such as 10, 100 or 1000. For example, if the division question is 5.32/5.6, you would multiply the divisor and dividend by 10 to get the equivalent division problem, 53.2/56. Completing this division will result in the exact same quotient as the original (try it on your calculator if you don't believe us). The main reason for completing decimal division in this way is to get the decimal in the correct location when using the U.S. long division algorithm.

A much simpler strategy, in our opinion, is to initially ignore the decimals all together and use estimation to place the decimal in the quotient. In the same example as above, you would complete 532/56 = 95. If you "flexibly" round the original, you will get about 5/5 which is about 1, so the decimal in 95 must be placed to make 95 close to 1. In this case, you would place it just before the 9 to get 0.95. Combining this strategy with the one above can also help a great deal with more difficult questions. For example, 4.584184 ÷ 0.461 can first be converted the to equivalent: 4584.184 ÷ 461 (you can estimate the quotient to be around 10). Complete the division question without decimals: 4584184 ÷ 461 = 9944 then place the decimal, so that 9944 is about 10. This results in 9.944.

Dividing decimal numbers doesn't have to be too difficult, especially with the worksheets below where the decimals work out nicely. To make these worksheets, we randomly generated a divisor and a quotient first, then multiplied them together to get the dividend. Of course, you will see the quotients only on the answer page, but generating questions in this way makes every decimal division problem work out nicely.

• Decimal Long Division with Quotients That Work Out Nicely Dividing Decimals by Various Decimals with Various Sizes of Quotients Dividing Decimals by 1-Digit Tenths (e.g. 0.72 ÷ 0.8 = 0.9) Dividing Decimals by 1-Digit Tenths with Larger Quotients (e.g. 3.2 ÷ 0.5 = 6.4) Dividing Decimals by 2-Digit Tenths (e.g. 10.75 ÷ 2.5 = 4.3) Dividing Decimals by 2-Digit Tenths with Larger Quotients (e.g. 387.75 ÷ 4.7 = 82.5) Dividing Decimals by 3-Digit Tenths (e.g. 1349.46 ÷ 23.8 = 56.7) Dividing Decimals by 2-Digit Hundredths (e.g. 0.4368 ÷ 0.56 = 0.78) Dividing Decimals by 2-Digit Hundredths with Larger Quotients (e.g. 1.7277 ÷ 0.39 = 4.43) Dividing Decimals by 3-Digit Hundredths (e.g. 31.4863 ÷ 4.61 = 6.83) Dividing Decimals by 4-Digit Hundredths (e.g. 7628.1285 ÷ 99.91 = 76.35) Dividing Decimals by 3-Digit Thousandths (e.g. 0.076504 ÷ 0.292 = 0.262) Dividing Decimals by 3-Digit Thousandths with Larger Quotients (e.g. 2.875669 ÷ 0.551 = 5.219)

These worksheets would probably be used for estimating and calculator work.

• Horizontally Arranged Decimal Division Random # Digits Random # Places
• European Format Dividing Decimals with Quotients That Work Out Nicely European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number

In the next set of questions, the quotient does not always work out well and may have repeating decimals. The answer key shows a rounded quotient in these cases.

• European Format Dividing Decimals by Whole Numbers European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number
• European Format Dividing Decimals by Decimals European Format Decimal Tenth (0,1 to 9,9) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Hundredth (0,01 to 9,99) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Thousandth (0,001 to 9,999) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Ten Thousandth (0,0001 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Various Decimal Places (1,1 to 9,9999)

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Fractions and Decimals Study Guide

Introduction to fractions.

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator .

Converting Fractions to Decimals

To convert a fraction to a decimal , divide the numerator by the denominator . For example, to convert 3/4 to a decimal , divide 3 by 4: 3 ÷ 4 = 0.75

Converting Decimals to Fractions

To convert a decimal to a fraction , write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places. For example, to convert 0.75 to a fraction : 0.75 = 75/100 = 3/4

Adding and Subtracting Fractions

To add or subtract fractions with the same denominator , simply add or subtract the numerators and keep the denominator the same. For fractions with different denominators , find a common denominator and then perform the operation.

Multiplying and Dividing Fractions

To multiply fractions , multiply the numerators and denominators together. To divide fractions , multiply the first fraction by the reciprocal of the second fraction .

Practice Problems

1. Convert the fraction 5/8 to a decimal . Answer: 5 ÷ 8 = 0.625

2. Convert the decimal 0.4 to a fraction . Answer: 0.4 = 4/10 = 2/5

3. Add the fractions 1/3 and 2/5. Answer: 1/3 + 2/5 = 5/15 + 6/15 = 11/15

4. Multiply the fractions 2/3 and 3/4. Answer: 2/3 * 3/4 = 6/12 = 1/2

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◂ Math Worksheets and Study Guides Fifth Grade. Fractions/Decimals

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Decimal Worksheets Hub Page

Welcome to our Decimal Worksheets area.

On this page, there are links to all of our decimal math worksheets, including decimal place value, decimal money worksheets and our adding, subtracting, multiplying and dividing decimals pages.

We also have some decimal resources including decimal place value charts to support teaching and learning of decimals.

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• This page contains links to other Math webpages where you will find a range of activities and resources.
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Decimal Worksheets

On this page you will find link to our range of decimal math worksheets.

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• Decimal Place Value Charts

Decimal Place Value Worksheets

Rounding decimals.

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Decimal Addition

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Converting Decimals

These decimal place value charts are designed to help children understand decimal place value.

They are especially useful in learning how to multiply and divide decimals by 10 or 100.

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Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp).

Using these sheets will help your child learn to:

• learn their place value with decimals up to 3dp;
• understand the value of each digit in a decimal number;
• learn to read and write numbers with up to 3dp.
• Decimal Place Value Worksheets to 2dp
• Decimal Place Value to 3dp
• Ordering Decimals Worksheets
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• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp
• Rounding Decimals Worksheet Challenges

Decimal Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 0.1;
• fill in the missing numbers in sequences;
• finding number bonds to 1 with numbers to 1dp, 2dp or 3dp.
• Counting By Decimals
• Decimal Number Bonds to 1
• Decimal Money Column Addition 4th Grade
• Decimal Column Addition 5th Grade

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Decimal Subtraction Worksheets

• Money Subtraction Worksheets ($)
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Decimal Multiplication Worksheets

These sheets are designed for 4th and 5th graders.

• Multiplying Decimals by 10 and 100
• Multiply and Divide by 10 100 (decimals)

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Chapter CR: Corequisite Review

Cr.2: fraction and decimal operations, learning outcomes.

• Add or Subtract fractions.
• Simplify fractions.
• Multiply fractions.
• Divide fractions.
• Round a decimal to a given place value
• Convert a decimal to a fraction or mixed number

Convert a percent to a decimal

Math students and working adults often find their knowledge of how to add, subtract, multiply, and divide fractions has grown rusty with disuse.  We tend to rely on calculators to do a lot of the work of fractions for us. College Algebra, though, builds up some important techniques for handling expressions and equations that are based on operations on fractions. So it is important to refamiliarize yourself with these skills. This section will remind you how to do operations on fractions. As you work through the rest of the course, you can return this section as needed for a quick reminder of operations on fractions.

Before we get started, let’s define some terminology.

• product:  the result of  multiplication
• factor: something being multiplied – for  [latex]3 \cdot 2 = 6[/latex] , both [latex]3[/latex] and [latex]2[/latex] are factors of [latex]6[/latex]
• numerator: the top part of a fraction – the numerator in the fraction [latex]\Large\frac{2}{3}[/latex] is [latex]2[/latex]
• denominator: the bottom part of a fraction – the denominator in the fraction [latex]\Large\frac{2}{3}[/latex] is [latex]3[/latex]

A Note About Instructions

Certain words are used in math textbooks and by teachers to provide students with instructions on what to do with a given problem. For example, you may see instructions such as find or simplify.  It is important to understand what these words mean so you can successfully work through the problems in this course. Here is a short list of some problem instructions along with their descriptions as they will be used in this module.

Add Fractions

When you need to add or subtract fractions, you will need to first make sure that the fractions have the same denominator. The denominator tells you how many pieces the whole has been broken into, and the numerator tells you how many of those pieces you are using.

The “parts of a whole” concept can be modeled with pizzas and pizza slices. For example, imagine a pizza is cut into [latex]4[/latex] pieces, and someone takes [latex]1[/latex] piece. Now, [latex]\Large\frac{1}{4}[/latex] of the pizza is gone and [latex]\Large\frac{3}{4}[/latex] remains. Note that both of these fractions have a denominator of [latex]4[/latex], which refers to the number of slices the whole pizza has been cut into. What if you have another pizza that had been cut into [latex]8[/latex] equal parts and [latex]3[/latex] of those parts were gone, leaving [latex]\Large\frac{5}{8}[/latex]?

How can you describe the total amount of pizza that is left with one number rather than two different fractions? You need a common denominator, technically called the least common multiple. Remember that if a number is a multiple of another, you can divide them and have no remainder.

One way to find the least common multiple of two or more numbers is to first multiply each by [latex]1, 2, 3, 4[/latex], etc.  For example, find the least common multiple of [latex]2[/latex] and [latex]5[/latex].

The smallest multiple they have in common will be the common denominator to use to rewrite each fraction into equivalent fractions. See the example below for a demonstration of our pizza problem.

One pizza, cut into four slices, has one missing. Another pizza of the same size has been cut into eight pieces, of which three have been removed. Describe the total amount of pizza left in the two pizzas using common terms.

Find the least common multiple of the denominators. This is the least common denominator.

Multiples of [latex]4: 4, \textbf{8},12,16, \textbf{24}[/latex]

Multiples of [latex]8: \textbf{8},16, \textbf{24}[/latex]

The least common denominator is [latex]8[/latex]—the smallest multiple they have in common.

Rewrite [latex]\dfrac{3}{4}[/latex] with a denominator of [latex]8[/latex]. You have to multiply both the top and bottom by [latex]2[/latex] so you don’t change the relationship between them.

[latex]\dfrac{3}{4}\cdot\dfrac{2}{2}=\dfrac{6}{8}[/latex]

We don’t need to rewrite [latex]\dfrac{5}{8}[/latex] since it already has the common denominator.

Both [latex]\dfrac{6}{8}[/latex] and [latex]\dfrac{5}{8}[/latex] have the same denominator, and you can describe how much pizza is left with common terms. Add the numerators and put them over the common denominator.

We have [latex]\dfrac{6}{8}[/latex] of the first pizza and [latex]\dfrac{5}{8}[/latex] of the second pizza left. That’s [latex]\dfrac{11}{8}[/latex] of an identically sized pizza, or [latex]1[/latex] and [latex]\dfrac{3}{8}[/latex], pizza still on the table.

To add fractions with unlike denominators, first rewrite them with like denominators. Then add or subtract the numerators over the common denominator.

Adding Fractions with Unlike Denominators

• Find a common denominator.
• Rewrite each fraction as an equivalent fraction using the common denominator.
• Now that the fractions have a common denominator, you can add the numerators.
• Simplify by canceling out all common factors in the numerator and denominator.

Simplify a Fraction

It is a common convention in mathematics to present fractions in lowest terms. We call this practice  simplifying or  reducing the fraction, and it can be accomplished by canceling (dividing) the common factors in a fraction’s numerator and denominator.  We can do this because a fraction represents division, and for any number [latex]a[/latex], [latex]\dfrac{a}{a}=1[/latex].

For example, to simplify [latex]\dfrac{6}{9}[/latex] you can rewrite [latex]6[/latex]and [latex]9[/latex] using the smallest factors possible as follows:

[latex]\dfrac{6}{9}=\dfrac{2\cdot3}{3\cdot3}[/latex]

Since there is a [latex]3[/latex] in both the numerator and denominator, and fractions can be considered division, we can divide the [latex]3[/latex] in the top by the [latex]3[/latex] in the bottom to reduce to [latex]1[/latex].

[latex]\dfrac{6}{9}=\dfrac{2\cdot\cancel{3}}{3\cdot\cancel{3}}=\dfrac{2\cdot1}{3}=\dfrac{2}{3}[/latex]

In the next example you are shown how to add two fractions with different denominators, then simplify the answer.

Add [latex]\Large\frac{2}{3}+\Large\frac{1}{5}[/latex]. Simplify the answer.

[latex]3\cdot5=15[/latex]

Rewrite each fraction with a denominator of [latex]15[/latex].

[latex]\begin{array}{c}\Large\frac{2}{3}\cdot\Large\frac{5}{5}=\Large\frac{10}{15}\\\\\Large\frac{1}{5}\cdot\Large\frac{3}{3}=\Large\frac{3}{15}\end{array}[/latex]

Add the fractions by adding the numerators and keeping the denominator the same. Make sure the fraction cannot be simplified.

[latex]\Large\frac{10}{15}+\Large\frac{3}{15}=\Large\frac{13}{15}[/latex]

[latex]\Large\frac{2}{3}+\Large\frac{1}{5}=\Large\frac{13}{15}[/latex]

You can find a common denominator by finding the common multiples of the denominators. The least common multiple is the easiest to use.

Add [latex]\Large\frac{3}{7}+\Large\frac{2}{21}[/latex]. Simplify the answer.

Multiples of [latex]7: 7, 14, \textbf{21}[/latex]

Multiples of [latex]21:\textbf{21}[/latex]

Rewrite each fraction with a denominator of [latex]21[/latex].

[latex]\begin{array}{c}\Large\frac{3}{7}\cdot\Large\frac{3}{3}=\Large\frac{9}{21}\\\\\Large\frac{2}{21}\end{array}[/latex]

[latex]\Large\frac{9}{21}+\Large\frac{2}{21}=\Large\frac{11}{21}[/latex]

[latex]\Large\frac{3}{7}+\Large\frac{2}{21}=\Large\frac{11}{21}[/latex]

In the following video you will see an example of how to add two fractions with different denominators.

You can also add more than two fractions as long as you first find a common denominator for all of them. An example of a sum of three fractions is shown below. In this example, you will use the prime factorization method to find the LCM.

Think About It

Add [latex]\Large\frac{3}{4}+\Large\frac{1}{6}+\Large\frac{5}{8}[/latex].  Simplify the answer and write as a mixed number.

What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would add three fractions with different denominators together.

[latex]4=2\cdot2\\6=3\cdot2\\8=2\cdot2\cdot2\\\text{LCM}:\,\,2\cdot2\cdot2\cdot3=24[/latex]

Rewrite each fraction with a denominator of [latex]24[/latex].

[latex]\begin{array}{c}\Large\frac{3}{4}\cdot\Large\frac{6}{6}=\Large\frac{18}{24}\\\\\Large\frac{1}{6}\cdot\Large\frac{4}{4}=\Large\frac{4}{24}\\\\\Large\frac{5}{8}\cdot\Large\frac{3}{3}=\Large\frac{15}{24}\end{array}[/latex]

Add the fractions by adding the numerators and keeping the denominator the same.

[latex]\Large\frac{18}{24}+\Large\frac{4}{24}+\Large\frac{15}{24}=\Large\frac{37}{24}[/latex]

Write the improper fraction as a mixed number and simplify the fraction.

[latex]\Large\frac{37}{24}=\normalsize 1\,\,\Large\frac{13}{24}[/latex]

[latex]\Large\frac{3}{4}+\Large\frac{1}{6}+\Large\frac{5}{8}=\normalsize 1\Large\frac{13}{24}[/latex]

Subtract Fractions

Subtracting fractions follows the same technique as adding them. First, determine whether or not the denominators are alike. If not, rewrite each fraction as an equivalent fraction, all having the same denominator.  Below are some examples of subtracting fractions whose denominators are not alike.

Subtract [latex]\Large\frac{1}{5}-\Large\frac{1}{6}[/latex]. Simplify the answer.

[latex]5\cdot6=30[/latex]

Rewrite each fraction as an equivalent fraction with a denominator of [latex]30[/latex].

[latex]\begin{array}{c}\Large\frac{1}{5}\cdot\Large\frac{6}{6}=\Large\frac{6}{30}\\\\\Large\frac{1}{6}\cdot\Large\frac{5}{5}=\Large\frac{5}{30}\end{array}[/latex]

Subtract the numerators. Simplify the answer if needed.

[latex]\Large\frac{6}{30}-\Large\frac{5}{30}=\Large\frac{1}{30}[/latex]

[latex]\Large\frac{1}{5}-\Large\frac{1}{6}=\Large\frac{1}{30}[/latex]

The example below shows how to use multiples to find the least common multiple, which will be the least common denominator.

Subtract [latex]\Large\frac{5}{6}-\Large\frac{1}{4}[/latex]. Simplify the answer.

Multiples of  [latex]6: 6, \textbf{12}, 18, 24[/latex]

Multiples of  [latex]4: 4, 8, \textbf{12},16, 20[/latex]

[latex]12[/latex] is the least common multiple of [latex]6[/latex] and [latex]4[/latex].

Rewrite each fraction with a denominator of [latex]12[/latex].

[latex]\begin{array}{c}\Large\frac{5}{6}\cdot\Large\frac{2}{2}=\Large\frac{10}{12}\\\\\Large\frac{1}{4}\cdot\Large\frac{3}{3}=\Large\frac{3}{12}\end{array}[/latex]

Subtract the fractions. Simplify the answer if needed.

[latex]\Large\frac{10}{12}-\Large\frac{3}{12}=\Large\frac{7}{12}[/latex]

[latex]\Large\frac{5}{6}-\Large\frac{1}{4}=\Large\frac{7}{12}[/latex]

In the following video you will see an example of how to subtract fractions with unlike denominators.

Multiply Fractions

Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with fractions.   There are many times when it is necessary to multiply fractions. A model may help you understand multiplication of fractions.

When you multiply a fraction by a fraction, you are finding a “fraction of a fraction.” Suppose you have [latex]\Large\frac{3}{4}[/latex] of a candy bar and you want to find [latex]\Large\frac{1}{2}[/latex] of the [latex]\Large\frac{3}{4}[/latex]:

By dividing each fourth in half, you can divide the candy bar into eighths.

Then, choose half of those to get [latex]\Large\frac{3}{8}[/latex].

In both of the above cases, to find the answer, you can multiply the numerators together and the denominators together.

Multiplying Two Fractions

[latex]\Large\frac{a}{b}\cdot\Large\frac{c}{d}=\Large\frac{a\cdot c}{b\cdot d}=\Large\frac{\text{product of the numerators}}{\text{product of the denominators}}[/latex]

Multiplying More Than Two Fractions

[latex]\Large\frac{a}{b}\cdot\Large\frac{c}{d}\cdot\Large\frac{e}{f}=\Large\frac{a\cdot c\cdot e}{b\cdot d\cdot f}[/latex]

Multiply [latex]\Large\frac{2}{3}\cdot\Large\frac{4}{5}[/latex]

[latex]\Large\frac{2\cdot 4}{3\cdot 5}[/latex]

Simplify, if possible. This fraction is already in lowest terms.

[latex]\Large\frac{8}{15}[/latex]

To review: if a fraction has common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.

For example,

• Given [latex]\Large\frac{8}{15}[/latex], the factors of [latex]8[/latex] are: [latex]1, 2, 4, 8[/latex] and the factors of [latex]15[/latex] are: [latex]1, 3, 5, 15[/latex].  [latex]\Large\frac{8}{15}[/latex] is simplified because there are no common factors of [latex]8[/latex] and [latex]15[/latex].
• Given [latex]\Large\frac{10}{15}[/latex], the factors of [latex]10[/latex] are: [latex]1, 2, 5, 10[/latex] and the factors of [latex]15[/latex] are: [latex]1, 3, 5, 15[/latex]. [latex]\Large\frac{10}{15}[/latex] is not simplified because [latex]5[/latex] is a common factor of [latex]10[/latex] and [latex]15[/latex].

You can simplify first, before you multiply two fractions, to make your work easier. This allows you to work with smaller numbers when you multiply.

In the following video you will see an example of how to multiply two fractions, then simplify the answer.

Multiply [latex]\Large\frac{2}{3}\cdot\Large\frac{1}{4}\cdot\Large\frac{3}{5}[/latex]. Simplify the answer.

What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would multiply three fractions together.

[latex]\Large\frac{2\cdot 1\cdot 3}{3\cdot 4\cdot 5}[/latex]

Simplify first by canceling (dividing) the common factors of [latex]3[/latex] and [latex]2[/latex]. [latex]3[/latex] divided by [latex]3[/latex] is [latex]1[/latex], and [latex]2[/latex] divided by  [latex]2[/latex] is [latex]1[/latex].

[latex]\begin{array}{c}\Large\frac{2\cdot 1\cdot3}{3\cdot (2\cdot 2)\cdot 5}\\\Large\frac{\cancel{2}\cdot 1\cdot\cancel{3}}{\cancel{3}\cdot (\cancel{2}\cdot 2)\cdot 5}\\\Large\frac{1}{10}\end{array}[/latex]

[latex]\Large\frac{2}{3}\cdot\Large\frac{1}{4}\cdot\Large\frac{3}{5}[/latex] = [latex]\Large\frac{1}{10}[/latex]

Divide Fractions

There are times when you need to use division to solve a problem. For example, if painting one coat of paint on the walls of a room requires [latex]3[/latex] quarts of paint and you have a bucket that contains [latex]6[/latex] quarts of paint, how many coats of paint can you paint on the walls? You divide [latex]6[/latex] by [latex]3[/latex] for an answer of [latex]2[/latex] coats. There will also be times when you need to divide by a fraction. Suppose painting a closet with one coat only required [latex]\Large\frac{1}{2}[/latex] quart of paint. How many coats could be painted with the 6 quarts of paint? To find the answer, you need to divide [latex]2[/latex] by the fraction, [latex]\Large\frac{1}{2}[/latex].

Before we begin dividing fractions, let’s cover some important terminology.

• reciprocal: two fractions are reciprocals if their product is [latex]1[/latex] (Don’t worry; we will show you examples of what this means.)
• quotient: the result of division

Dividing fractions requires using the reciprocal of a number or fraction. If you multiply two numbers together and get [latex]1[/latex] as a result, then the two numbers are reciprocals. Here are some examples of reciprocals:

Sometimes we call the reciprocal the “flip” of the other number: flip [latex]\Large\frac{2}{5}[/latex] to get the reciprocal [latex]\Large\frac{5}{2}[/latex].

Division by Zero

You know what it means to divide by [latex]2[/latex] or divide by [latex]10[/latex], but what does it mean to divide a quantity by [latex]0[/latex]? Is this even possible? Can you divide [latex]0[/latex] by a number? Consider the fraction

[latex]\Large\frac{0}{8}[/latex]

We can read it as, “zero divided by eight.” Since multiplication is the inverse of division, we could rewrite this as a multiplication problem.

[latex]\text{?}\cdot{8}=0[/latex].

We can infer that the unknown must be [latex]0[/latex] since that is the only number that will give a result of [latex]0[/latex] when it is multiplied by [latex]8[/latex].

Now let’s consider the reciprocal of [latex]\Large\frac{0}{8}[/latex] which would be [latex]\Large\frac{8}{0}[/latex]. If we rewrite this as a multiplication problem, we will have

[latex]\text{?}\cdot{0}=8[/latex].

This doesn’t make any sense. There are no numbers that you can multiply by zero to get a result of 8. The reciprocal of [latex]\Large\frac{8}{0}[/latex] is undefined, and in fact, all division by zero is undefined.

Divide a Fraction by a Whole Number

When you divide by a whole number, you are multiplying by the reciprocal. In the painting example where you need [latex]3[/latex] quarts of paint for a coat and have [latex]6[/latex] quarts of paint, you can find the total number of coats that can be painted by dividing [latex]6[/latex] by [latex]3[/latex], [latex]6\div3=2[/latex]. You can also multiply [latex]6[/latex] by the reciprocal of [latex]3[/latex], which is [latex]\Large\frac{1}{3}[/latex], so the multiplication problem becomes

[latex]\Large\frac{6}{1}\cdot\Large\frac{1}{3}=\Large\frac{6}{3}=\normalsize2[/latex]

Dividing is Multiplying by the Reciprocal

For all division, you can turn the operation into multiplication by using the reciprocal. Dividing is the same as multiplying by the reciprocal.

The same idea will work when the divisor (the thing being divided) is a fraction. If you have [latex]\Large\frac{3}{4}[/latex] of a candy bar and need to divide it among [latex]5[/latex] people, each person gets [latex]\Large\frac{1}{5}[/latex] of the available candy:

[latex]\Large\frac{1}{5}\normalsize\text{ of }\Large\frac{3}{4}=\Large\frac{1}{5}\cdot\Large\frac{3}{4}=\Large\frac{3}{20}[/latex]

Each person gets [latex]\Large\frac{3}{20}[/latex] of a whole candy bar.

If you have a recipe that needs to be divided in half, you can divide each ingredient by [latex]2[/latex], or you can multiply each ingredient by [latex]\Large\frac{1}{2}[/latex] to find the new amount.

For example, dividing by [latex]6[/latex] is the same as multiplying by the reciprocal of [latex]6[/latex], which is [latex]\Large\frac{1}{6}[/latex]. Look at the diagram of two pizzas below.  How can you divide what is left (the red shaded region) among [latex]6[/latex] people fairly?

Each person gets one piece, so each person gets [latex]\Large\frac{1}{4}[/latex] of a pizza.

Dividing a fraction by a whole number is the same as multiplying by the reciprocal, so you can always use multiplication of fractions to solve division problems.

Find [latex]\Large\frac{2}{3}\div \normalsize 4[/latex]

Dividing by [latex]4[/latex] or [latex]\Large\frac{4}{1}[/latex] is the same as multiplying by the reciprocal of [latex]4[/latex], which is [latex]\Large\frac{1}{4}[/latex].

[latex]\Large\frac{2}{3}\normalsize\div 4=\Large\frac{2}{3}\cdot\Large\frac{1}{4}[/latex]

Multiply numerators and multiply denominators.

[latex]\Large\frac{2\cdot 1}{3\cdot 4}=\Large\frac{2}{12}[/latex]

Simplify to lowest terms by dividing numerator and denominator by the common factor [latex]4[/latex].

[latex]\Large\frac{1}{6}[/latex]

[latex]\Large\frac{2}{3}\normalsize\div4=\Large\frac{1}{6}[/latex]

Divide. [latex] 9\div\Large\frac{1}{2}[/latex]

Dividing by [latex]\Large\frac{1}{2}[/latex] is the same as multiplying by the reciprocal of [latex]\Large\frac{1}{2}[/latex], which is [latex]\Large\frac{2}{1}[/latex].

[latex]9\div\Large\frac{1}{2}=\Large\frac{9}{1}\cdot\Large\frac{2}{1}[/latex]

[latex]\Large\frac{9\cdot 2}{1\cdot 1}=\Large\frac{18}{1}=\normalsize 18[/latex]

This answer is already simplified to lowest terms.

[latex]9\div\Large\frac{1}{2}=\normalsize 18[/latex]

Divide a Fraction by a Fraction

Sometimes you need to solve a problem that requires dividing by a fraction. Suppose you have a pizza that is already cut into [latex]4[/latex] slices. How many [latex]\Large\frac{1}{2}[/latex] slices are there?

There are [latex]8[/latex] slices. You can see that dividing [latex]4[/latex] by [latex]\Large\frac{1}{2}[/latex] gives the same result as multiplying [latex]4[/latex] by [latex]2[/latex].

What would happen if you needed to divide each slice into thirds?

You would have [latex]12[/latex] slices, which is the same as multiplying [latex]4[/latex] by [latex]3[/latex].

Dividing with Fractions

• Find the reciprocal of the number that follows the division symbol.
• Multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol).

Any easy way to remember how to divide fractions is the phrase “keep, change, flip.” This means to KEEP the first number, CHANGE the division sign to multiplication, and then FLIP (use the reciprocal) of the second number.

Divide [latex]\Large\frac{2}{3}\div\Large\frac{1}{6}[/latex]

KEEP [latex]\Large\frac{2}{3}[/latex]

CHANGE   [latex] \div [/latex] to  [latex]\cdot[/latex]

FLIP  [latex]\Large\frac{1}{6}[/latex]

[latex]\Large\frac{2}{3}\cdot\Large\frac{6}{1}[/latex]

[latex]\Large\frac{2\cdot6}{3\cdot1}=\Large\frac{12}{3}[/latex]

[latex]\Large\frac{12}{3}=\normalsize 4[/latex]

[latex]\Large\frac{2}{3}\div\Large \frac{1}{6}=\normalsize 4[/latex]

Divide [latex]\Large\frac{3}{5}\div\Large\frac{2}{3}[/latex]

[latex]\Large\frac{3}{5}\cdot\Large\frac{3}{2}[/latex]

[latex]\Large\frac{3\cdot 3}{5\cdot 2}=\Large\frac{9}{10}[/latex]

[latex]\Large\frac{3}{5}\div\Large\frac{2}{3}=\Large\frac{9}{10}[/latex]

When solving a division problem by multiplying by the reciprocal, remember to write all whole numbers and mixed numbers as improper fractions. The final answer should be simplified and written as a mixed number.

In the following video you will see an example of how to divide an integer by a fraction, as well as an example of how to divide a fraction by another fraction.

Rounding Decimals

Round a decimal.

• Locate the given place value and mark it with an arrow.
• Underline the digit to the right of the given place value.
• Yes – add [latex]1[/latex] to the digit in the given place value.
• No – do not change the digit in the given place value
• Rewrite the number, removing all digits to the right of the given place value.

Round [latex]18.379[/latex] to the nearest hundredth.

Round [latex]18.379[/latex] to the nearest ⓐ tenth ⓑ whole number.

Watch the following video to see an example of how to round a number to several different place values.

Converting a Decimal to a Fraction

Convert a decimal number to a fraction or mixed number..

• If it is zero, the decimal converts to a proper fraction.
• Write the whole number.
• Determine the place value of the final digit.
• numerator—the ‘numbers’ to the right of the decimal point
• denominator—the place value corresponding to the final digit
• Simplify the fraction, if possible.

Write each of the following decimal numbers as a fraction or a mixed number:

ⓐ [latex]4.09[/latex]

ⓑ [latex]3.7[/latex]

ⓒ [latex]-0.286[/latex]

Did you notice that the number of zeros in the denominator is the same as the number of decimal places?

In the next video example, we who how to convert a decimal into a fraction. Examples: Write a Number in Decimal Notation from Words.

Converting a Percent to a Decimal

To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.

• Write the percent as a ratio with the denominator [latex]100[/latex].
• Convert the fraction to a decimal by dividing the numerator by the denominator.

Convert each percent to a decimal:

ⓐ [latex]\text{6%}[/latex] ⓑ [latex]\text{78%}[/latex]

Solution Because we want to change to a decimal, we will leave the fractions with denominator [latex]100[/latex] instead of removing common factors.

ⓐ [latex]\text{9%}[/latex] ⓑ [latex]\text{87%}[/latex]

ⓐ [latex]0.09[/latex] ⓑ [latex]0.87[/latex]

ⓐ [latex]\text{135%}[/latex] ⓑ [latex]\text{12.5%}[/latex]

Ch 2: Fractions & Decimals, Notes and Homework (Google Files)

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Ch 2: Fractions and Decimals, Notes and Homework , Big Ideas Math MRL, 6th Grade

This is a guided notes and homework set that includes 10 math problems, 12 math problems, and a modified version of each homework. The modified homework problems are broken down into smaller steps, with each step being more basic than the last. This can help students who are struggling to understand the material by providing them with more support and help them to work through the problem one step at a time.

This unit covers the following concepts:

• Section 2.1 Multiplying Fractions
• Section 2.2 Dividing Fractions
• Section 2.3 Dividing Mixed Numbers
• Section 2.4 Adding and Subtracting Decimals
• Section 2.5 Multiplying Decimals
• Section 2.6 Dividing Whole Numbers
• Section 2.7 Dividing Decimals

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Convert Fractions to Decimals

The simplest method is to use a calculator.

Just divide the top of the fraction by the bottom, and read off the answer!

Example : What is 5 8 as a decimal ... ?

... get your calculator and type in "5 / 8 ="

The answer should be 0.625

No Calculator? Use Long Division to Decimal Places

Example: here is what long division of 5 8 looks like:.

In that case we inserted extra zeros and did 5.000 8 to get 0.625

Read the Long Division to Decimal Places page for more details.

Another Method

Yet another method you may like is to follow these steps:.

• Step 1 : Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s .
• Step 2 : Multiply both top and bottom by that number.
• Step 3 . Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)

Example: Convert 3 4 to a Decimal

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25:

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);

Answer = 0.75

Example: Convert 3 16 to a Decimal

Step 1: We have to multiply 16 by 625 to become 10,000

Step 2: Multiply top and bottom by 625:

Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);

Answer = 0.1875

Example: Convert 1 3 to a Decimal

Step 1: There is no way to multiply 3 to become 10 or 100 or any "1 followed by 0s", but we can calculate an approximate decimal by choosing to multiply by, say, 333

Step 2: Multiply top and bottom by 333:

Step 3: Now, 999 is nearly 1,000 , so let us write down 333 with the decimal point 3 spaces from the right (because 1,000 has 3 zeros):

Answer = 0.333 (accurate to only 3 decimal places!)

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Fractions to/from Decimals for Grade 4

Converting fractions to and from decimals worksheets.

These worksheets provide introductory exercises for converting fractions to and from decimals .  All fractions have a denominator of 10 or 100 for easy translation into decimals.  Mixed numbers are also used.

Sample Grade 4 converting fractions to decimals worksheet

More decimals worksheets

Find all of our decimals worksheets , from converting fractions to decimals to long division of multi-digit decimal numbers.

More fractions worksheets

Explore all of our fractions worksheets , from dividing shapes into "equal parts" to multiplying and dividing improper fractions and mixed numbers.

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Question: Ordering fractions and decimals Order these numbers from least to greatest. 7(11)/(20),8.291,7.29,(15)/(2)

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