subtracting fractions problem solving questions

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Subtracting Fractions Worksheets

Welcome to our Subtracting Fractions Worksheets page. We have a range of worksheets designed to help students learn to subtract fractions with both like and unlike denominators.

Our sheets range in difficulty from easier supported sheets with like denominators to harder sheets with different denominators and improper fractions.

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• Steps to Subtract Fractions support
• All Subtracting Fractions Worksheets
• Subtracting Fractions with Like Denominators Worksheets
• Subtracting Fractions with Like Denominators Quiz
• Subtracting Fractions (with Unlike Denominators) Worksheets
• Subtracting Improper Fractions (unlike denominators)
• Subtracting Fractions (with Unlike Denominators) Quiz
• More related Math resources

Steps to Subtract Fractions Support

Here you will find support pages and our subtracting fraction calculator to help you to learn about how to subtract fractions.

For those of you who like to see some algebra, here is the simple formula for subtracting two fractions:

Formula for subtracting two fractions

\[{a \over b} - {c \over d} = {ad - bc \over bd} \]

• Steps to Subtract Fractions support page

• Subtracting Fractions Calculator

Here you will find a selection of Fraction worksheets designed to help your child practice how to subtract fractions.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

Next to each sheet is a description of the math skills involved.

Using these sheets will help your child to:

• apply their understanding of equivalent fractions;
• subtract fractions with like denominators;
• subtract fractions with different denominators;
• subtract improper fractions with different denominators.

These skills and worksheets are aimed at 3rd through to 7th grade.

The easiest sheets with like denominators are suitable for 3rd graders (sheet 1)

The hardest sheets with subtracting improper fractions with different denominators are more suitable for 7th graders.

Subtracting Fractions (like denominators)

If you are looking to subtract fractions which have the same denominator, take a look at our sheets below.

Like Denominators

Sheet 1: the easiest sheet, no simplifying or converting needed.

• Subtracting Fractions with like denominators 1
• PDF version

Sheet 2: like denominators; simplifying needed.

• Subtracting Fractions with like denominators 2

Sheet 3: like denominators; simplifying and/or converting to a mixed number.

• Subtracting Fractions with like denominators 3

Subtract Fractions with Like Denominators Quiz

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This quick quiz tests your knowledge and skill at subtracting fractions with like denominators.

Subtracting Fractions unlike denominators

Sheet 1: easy to convert denominators with one denominator a multiple of the other; no simplifying or converting needed

• Subtracting Fractions unlike denominators 1

Sheet 2: easy to convert denominators with one denominator a multiple of the other; simplifying needed

• Subtracting Fractions unlike denominators 2

Sheet 3: easy to convert denominators; simplifying and/or converting to a mixed number needed

• Subtracting Fractions unlike denominators 3

Sheet 4: harder to convert denominators; no simplifying or converting needed

• Subtracting Fractions unlike denominators 4

Sheet 5: harder to convert denominators; simplifying needed

• Subtracting Fractions unlike denominators 5

Sheet 6: harder to convert denominators; simplifying and/or converting needed

• Subtracting Fractions unlike denominators 6

Subtracting Improper Fractions unlike denominators

Sheet 1: hard to convert denominators; simplifying and/or converting needed

• Subtracting Improper Fractions Sheet 1

Subtracting Mixed Fractions unlike denominators

• Subtracting Mixed Fractions Sheet 1

Subtracting Fractions (with unlike) Denominators Quiz

This quick quiz tests your knowledge and skill at subtracting a range of fractions.

More Recommended Math Resources

Take a look at some more of our resources similar to these.

More Adding and Subtracting Fractions Sheets

Adding and subtracting fractions works differently from adding and subtracting integers or decimals.

If the two fractions have the same denominator, then it is quite easy to add or subtract the fractions by simply adding the numerators together.

If the fractions have different denominators, then they need to be changed into equivalent fractions with the same denominator before they can be added or subtracted.

The printable learning fractions pages below contains more support, examples and practice adding and subtracting fractions.

• Subtracting Fractions with like denominators (easier)

• How do you Add Fractions support page
• Adding Fractions Worksheets
• Adding Improper Fractions
• Adding & Subtracting Fractions Worksheets
• Fractions Adding and Subtracting Worksheets (randomly generated)
• Equivalent Fractions Worksheets

This is a pre-requisite for knowing how to add and subtract fractions.

• develop an understanding of equivalent fractions;
• know when two fractions are equivalent;
• find a fraction that is equivalent to another.

Multiplying and Dividing Fractions

• multiply and divide fractions by whole numbers and other fractions;
• multiply and divide mixed fractions.
• Multiplying Fractions Worksheets
• Multiplying Mixed Fractions
• How to Divide Fractions
• Dividing Fractions by whole numbers
• How to Divide Mixed Numbers
• Least Common Multiple Calculator

Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.

It will tell you the best multiple to convert the denominators of the fractions you are subtracting into.

There are also some worked examples.

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Subtracting Fractions Questions

Subtracting fractions questions given here cover all types of fractions including like, unlike and mixed. These involve both numerical and word problems of subtracting fractions. Practising various questions on subtracting fractions will enhance your understanding of performing various arithmetic operations on fractions. Let’s learn how to subtract fractions using the solved problems given below.

What is the Subtraction of Fractions?

In mathematics, the subtraction of fractions involves finding the difference between two or more fractions with the same denominators or different denominators. The subtraction of fractions involves the following cases.

• Subtracting fractions from whole numbers
• Subtracting fractions with the same denominator
• Subtracting fractions with different denominators
• Subtracting mixed fractions

Also, check: Subtracting fractions

Subtracting Fractions Questions and Answers

1. Subtract: 3 – (4/13)

3 – (4/13)

Here, 3 is a whole number and 4/13 is a fraction.

= (39 – 4)/13

Therefore, 3 – (4/13) = 35/13

2. Evaluate the following:

(i) (9/14) – (5/14)

(ii) (7/10) – (3/10)

Here, the denominators are the same, i.e., they are like fractions.

Thus, (9/14) – (5/14) = (9 – 5)/14

On further simplification, we have;

(9/14) – (5/14) = 4/14 = 2/7

= (7 – 3)/10

Thus, (7/10) – (3/10) = 4/10 = ⅖

3. Compute the following.

(i) (10/12) – (⅓)

(ii) (⅔) – (5/20)

= (⅚) – (⅓)

By taking the LCM of denominators, we have;

= (5 – 2)/6

Therefore, (10/12) – (⅓) = ½

= (⅔) – (¼)

= (8 – 3)/12

Therefore, (⅔) – (5/20) = 5/12

4. Find the value of \(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}\end{array} \) .

\(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}\end{array} \)

Here, both terms are mixed fractions.

Let’s convert the mixed fractions into improper fractions.

\(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}\\=\frac{131}{9}-\frac{322}{15}\\=\frac{655-966}{45}\\=\frac{-311}{45}\\=-6\frac{41}{45} \end{array} \)

Therefore, \(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}=-6\frac{41}{45} \end{array} \)

5. Subtract 5 from 11 ⅗.

11 ⅗ – 5

Here, 11 ⅗ is a mixed fraction.

11 ⅗ = (11 × 5 + 3)/5 = 58/5

Now, 11 ⅗ – 5

= (58/5) – 5

= (58 – 25)/5

Therefore, 11 ⅗ – 5 = 33/5.

6. Find the value of (23/4) – (5/3).

(23/4) – (5/3)

By taking the LCM of denominators, we get;

= (23 × 3 – 5 × 4)/12

= (69 – 20)/12

Thus, (23/4) – (5/3) – 4 1/12.

7. Evaluate: \(\begin{array}{l}\frac{4}{3}-\left ( 1\frac{11}{12}-\frac{5}{4} \right )\end{array} \) .

\(\begin{array}{l}\frac{4}{3}-\left ( 1\frac{11}{12}-\frac{5}{4} \right )\\=\frac{4}{3}-\left ( \frac{23}{12}-\frac{5}{4} \right )\\=\frac{4}{3}-\left ( \frac{23-15}{12}\right )\\=\frac{4}{3}-\frac{8}{12}\\=\frac{4}{3}-\frac{2}{3}\\=\frac{4-2}{3}\\=\frac{2}{3}\end{array} \)

8. A father leaves his money to his four children. The first received 1/3, the second received 1/6, and the third received 2/5. How much did the remaining child receive (assume that the total money is one whole)?

Total money = 1

The amount received by the first child = 1/3

The amount received by the second child = 1/6

The amount received by the third child = 2/5

The amount received by the last child = 1 – (1/3) – (1/6) – (2/5)

= (30 – 10 – 5 – 12)/30 {since the LCM of 3, 6, and 5 is 30}

= (30 – 27)/30

Thus, the remaining child will receive 1/10th of the father’s money.

9. Vinu worked for 14/3 hours on Friday and his friend Shan worked for 25/6 hours. How many more hours than Shan did Vinu work?

Number of hours worked by Vinu = 14/3

Number of hours worked by Shan = 25/6

Difference = 14/3 – 25/6

= (28 – 25)/6

Thus, Vinu worked ½ hour, i.e., half an hour more than Shan.

10. Arnav bought some sweets that weighed 4 2/3 kg. If he gave 3 1/6 kg to his friends, what is the amount of sweets he has left?

Sweets bought by Arnav = 4 2/3 kg

Sweets given to his friends = 3 1/6 kg

Sweets left with Arnav = 4 2/3 – 3 1/6

= 14/3 – 19/6

= (28 – 19)/6

Therefore, Arnav is left with 1 1/2 kg of sweets.

Practice Questions on Subtracting Fractions

• Calculate the following: (i) (9/11) – (½) (ii) (11/12) – (⅚)
• Subtract 6 ⅘ from 7.
• A jar contains 1 2/5 litres of mango juice. Kevin pours 4/15 litres of the juice into a glass. How much mango juice is left in the jar?
• David cleaned about 3/5 of the school lawn on Saturday. He cleaned another 1/4th of the lawn on Sunday. How much of the lawn is left to clean?
• Subtract: 3 7/12 – 1 2/6

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Add and Subtract Fractions Online practice for grades 3-7

On this page, you can practice addition and subtraction of fractions. Each practice set will automatically include both addition and subtraction problems.

The options are:

• You can limit the fractions in the problems to like fractions (fractions with the same denominator), for example: 1/6 + 4/6.
• You can limit the script to use only proper fractions—fractions that are less than 1. With this option, the script will make problems such as 1/4 + 2/5, but will not make problems such as 8/5 − 4/5.
• When you choose problems that use simplified fractions, the script will only include fractions in the problems that are in lowest terms. For example, you could get a problem such as 5/6 + 3/5, but you would not see 2/4 + 6/8.
• The last option, when chose, allows or accepts answers to not be in lowest terms. In other words, the script will accept an answer such as 8/10.

Note: ALL answers have to be given as mixed numbers, when possible. In other words, your answer cannot be left as an improper fraction.

You may use the space below to write the intermediate step. Your work in this area will not be checked.

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Fractions  - Adding and Subtracting Fractions

Fractions  -, adding and subtracting fractions, fractions adding and subtracting fractions.

Fractions: Adding and Subtracting Fractions

Lesson 3: adding and subtracting fractions.

/en/fractions/comparing-and-reducing-fractions/content/

Adding and subtracting fractions

In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water.

In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions.

Click through the slideshow to learn how to set up addition and subtraction problems with fractions.

Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter.

You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together.

When you add fractions, you just add the top numbers, or numerators .

That's because the bottom numbers, or denominators , show how many parts would make a whole.

We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total.

So we only need to add the numerators of our fractions.

We can stack the fractions so the numerators are lined up. This will make it easier to add them.

And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added.

We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work.

If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out.

Just like when we added, we'll stack our fractions to keep the numerators lined up.

This is because we want to subtract 1 part from 3 parts.

Now that our example is set up, we're ready to subtract!

Try setting up these addition and subtraction problems with fractions. Don't try solving them yet!

You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile.

You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner.

Your gas tank is 2/5 full, and you put in another 2/5 of a tank.

Solving addition problems with fractions

Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions.

Click through the slideshow to learn how to add fractions.

Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.

Remember, when we add fractions, we don't add the denominators.

This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 .

3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added.

The denominators will stay the same, so we'll write 5 on the bottom of our new fraction.

3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake.

Let's try another example: 7/10 plus 2/10 .

Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 .

7 plus 2 equals 9 , so we'll write that to the right of the numerators.

Just like in our earlier example, the denominator stays the same.

So 7/10 plus 2/10 equals 9/10 .

Try solving some of the addition problems below.

Solving subtraction problems with fractions

Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too!

Click through the slideshow to learn how to subtract fractions.

Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.

Just like in addition, we're not going to change the denominators.

We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left.

We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators.

Just like when we added, the denominator of our answer will be the same as the other denominators.

So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home.

Let's try solving another problem: 5/6 minus 3/6 .

We'll start by subtracting the numerators.

5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators.

As usual, the denominator stays the same.

So 5/6 minus 3/6 equals 2/6 .

Try solving some of the subtraction problems below.

After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 .

Adding fractions with different denominators

On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup.

In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD .

We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual.

Click through the slideshow to learn how to add fractions with different denominators.

Let's add 1/4 and 1/3 .

Before we can add these fractions, we'll need to change them so they have the same denominator .

To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 .

It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD .

Since 12 is the LCD, it will be the new denominator for our fractions.

Now we'll change the numerators of the fractions, just like we changed the denominators.

First, let's look at the fraction on the left: 1/4 .

To change 4 into 12 , we multiplied it by 3 .

Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 .

1 times 3 equals 3 .

1/4 is equal to 3/12 .

Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well.

Our old denominator was 3 . We multiplied it by 4 to get 12.

We'll also multiply the numerator by 4 . 1 times 4 equals 4 .

So 1/3 is equal to 4/12 .

Now that our fractions have the same denominator, we can add them like we normally do.

3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 .

Try solving the addition problems below.

Subtracting fractions with different denominators

We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator.

Click through the slideshow to learn how to subtract fractions with different denominators.

Let's try subtracting 1/3 from 3/5 .

First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator .

It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD.

Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 .

5 times 3 equals 15 . So our fraction is now 9/15 .

Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 .

Now that our fractions have the same denominator, we can subtract like we normally do.

9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 .

Try solving the subtraction problems below.

Adding and subtracting mixed numbers

Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?

In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same.

5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first.

Let's add these two mixed numbers: 2 3/5 and 1 3/5 .

We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 .

As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 .

2 times 5 equals 10 .

Now, let's add 10 to the numerator, 3 .

10 + 3 equals 13 .

Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 .

Now we'll need to convert our second mixed number: 1 3/5 .

First, we'll multiply the whole number by the denominator. 1 x 5 = 5 .

Next, we'll add 5 to the numerators. 5 + 3 = 8 .

Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 .

Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.

13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 .

Because we started with a mixed number, let's convert this improper fraction back into a mixed number.

As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 .

The answer, 4, will become our whole number.

And the remainder , 1, will become the numerator of the fraction.

So 2 3/5 + 1 3/5 = 4 1/5 .

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Subtracting Fractions Word Problems Worksheets

Thumb through our printable subtracting fractions word problems worksheets and discover a treasure of fun, realistic scenarios. Our pdf prepping tools, with included answer keys, are well-chosen for grade 3 through grade 6 students. Task young learners with reading, understanding, and solving an array of fraction subtraction word problems. Deftly find the difference between two like fractions, two unlike fractions, mixed numbers, and more. Go after our free subtracting fractions word problems worksheet!

Subtracting Fractions with Whole Numbers Word Problems

Perk up your math sessions with this section of our subtracting fractions word problems worksheets. Have kids determining the difference between fractions and whole numbers in real life with nuance and flair!

• Download the set

Subtracting Like Fractions Word Problems

Pride yourself on your subtraction on fractions skills! The interactive scenarios in our pdf word problems worksheets for 3rd grade, 4th grade, and 5th grade make subtracting like fractions a rewarding affair!

Subtracting Unlike Fractions Word Problems

Enhance problem-solving skills with these fraction subtraction word problems worksheets. Young learners read and solve word problems involving fractions with different denominators with accuracy.

Subtracting Mixed Numbers Word Problems | Like Denominators

Do nothing by halves! Get kids going all out to subtract mixed numbers having same denominators! The key to solving these problems is finding the difference between the whole number parts and fractions separately.

Subtracting Mixed Numbers Word Problems | Unlike Denominators

Add bells and whistles to your fraction subtraction practice with our printables. Grade 4, grade 5, and grade 6 kids find the LCM of different denominators and obtain the difference between two mixed numbers.

Related Worksheets

» Subtracting Like Fractions

» Subtracting Unlike Fractions

» Subtracting Mixed Numbers

» Subtracting Fractions from Whole Numbers

» Fraction Word Problems

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Subtracting fractions word problems

Subtracting fractions word problems: 4 real-life examples.

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• Subtracting Fractions Word Problems

Introduction to Subtracting Fractions

Subtraction of fractions is an arithmetic operation to find the difference between two fractions. To subtract two like fractions, we have to subtract their numerators and write the difference over the common denominator . To subtract two unlike fractions, we must first convert them into like fractions by taking the LCM of the denominators. We can also subtract a whole number and fraction by writing the whole number in fractional form, for example, $3 = \dfrac{3}{1}$. Let us learn more about subtracting fractions and fraction subtraction problems in detail in this article.

How to Subtract Fractions?

Fractions are referred to as a part of a whole. A group of fractions can be classified as like fractions and unlike fractions based on the denominator value . Like fractions are those that have the same denominator. For example, $\dfrac{3}{4}$ and $\dfrac{5}{4}$. While unlike fractions are those that have different denominators, for example, $\dfrac{2}{3}$ and $\dfrac{4}{7}$. We can find the difference between two like fractions, unlike fractions and fractions and whole numbers .

The steps for subtracting fractions are listed below:

Step 1: Identify whether the given fractions have the same denominator or different denominators.

Step 2: In the case of like fractions, subtract the numerators and write their difference over the common denominator. For example, $\dfrac{5}{7} - \dfrac{2}{7} = \dfrac{5 - 2}{7} = \dfrac{3}{7}$.

On the other hand, unlike fractions, find the LCM of the denominators.

Step 3: Multiply the numerator and denominator of each fraction with a whole number to get the LCM in the denominator. It is done to convert unlike fractions to like fractions.

Step 4: Subtract their numerators and write the difference over the common denominator.

This is how we subtract two fractions.

Subtracting Fractions with Like Denominators

Fractions with the same denominator can be easily subtracted. To subtract fractions with the same denominators, follow the given steps:

Subtract the numerator.

Write the common denominator as the denominator of the resulting fraction.

Now, reduce the result to the lowest fraction, if possible.

Example: $\dfrac{4}{5}-\dfrac{2}{5}=\dfrac{2}{5}$

Subtraction of Fractions with Unlike Denominators

Two fractions with different or unequal denominators can be subtracted by following these steps:

First, take the LCM of the denominators.

We convert the given fractions to like fractions with the denominator as the LCM.

Now, subtract the numerators and write their difference over the common denominator.

Simplify, if needed.

Subtracting Fractions with Whole Numbers

Just like you have subtracted two fractions, you can also subtract fractions from whole numbers and vice-versa. Any integer can be written in fractional form by writing 1 as the denominator. For example, 7 can be written as $\dfrac{7}{1}$. Therefore, to subtract fractions and whole numbers, write them in the fractional form first. Then you can easily find the difference using the same rules for subtracting two unequal fractions. Consider the following example of subtracting a fraction from an integer: $2 - \dfrac{1}{4}$

Convert the integer, 2 to fractional form, i.e. $\dfrac{2}{1}$

Now, to subtract $\dfrac{2}{1} - \dfrac{1}{4}$, the least common multiple of 1 and 4 is 4. Multiply the numerator and denominator of $\dfrac{2}{1}$ by 4 to get 4 in the denominator.

$\dfrac{2}{1} - \dfrac{1}{4}$

= $\dfrac{2 \times 4}{1 \times 4} - \dfrac{1}{4}$

= $\dfrac{8}{4} - \dfrac{1}{4}$

= $\dfrac{7}{4}$

Thus, the subtraction of an integer and fraction, $2 - \dfrac{1}{4} = \dfrac{7}{4}$.

Solved Word Problems on Fraction Subtraction

Q 1. Jack jumped $4 \dfrac{1}{7}$ m in the long jump competition. Shane jumped $3 \dfrac{2}{9}$ m. Who jumped longer, and how many meters?

Ans: Jack jumped $=4 \dfrac{1}{7} \mathrm{~m}=\dfrac{29}{7} \mathrm{~m}=\dfrac{261}{63} \mathrm{~m}$

Shane jumped $=3 \dfrac{2}{9} \mathrm{~m}=\dfrac{29}{9} \mathrm{~m}=\dfrac{203}{63} \mathrm{~m}$

Because $261>203$, Jack jumped more.

$\text { Difference }=\dfrac{261}{63} \mathrm{~m}-\dfrac{203}{63} \mathrm{~m}$

$=\dfrac{261-203}{63} \mathrm{~m}$

$=\dfrac{58}{63} \mathrm{~m}$

Therefore, Jack jumped $\dfrac{58}{63} \mathrm{~m}$ more than Shane.

Q 2. Mary gave $\dfrac{1}{8}$ part of her money to Shelly. What fraction of money is left with her?

Ans: Money given to Shelly $=\dfrac{1}{8}$

Remaining money $=1-\dfrac{1}{8}$

$=\dfrac{1}{1}-\dfrac{1}{8}$

$=\dfrac{8}{8}-\dfrac{1}{8}$

$=\dfrac{7}{8}$

Thus, the fraction of money left is $=\dfrac{7}{8}$.

Fraction Subtraction Problems for Practice

Q 1. Sharon spent $4 \dfrac{3}{7}$ hours studying maths and playing tennis. How long did she study if she played tennis for $2 \dfrac{1}{4}$ hours?

Ans: $\dfrac{61}{28}$

Q 2. Rex had some money. He spent $\dfrac{1}{6}$ of it on Monday, $\dfrac{3}{8}$ on Thursday, and $\dfrac{1}{4}$ on Wednesday. What part of the money is still left with him?

Ans: $\dfrac{5}{24}$.

Q 3. Ron used $3 \dfrac{1}{4}$ litres of paint from a tin of $5 \dfrac{1}{2}$, to colour the walls of his room. What fraction of paint is still left in the tin?

Ans: $\dfrac{9}{4}$ litres.

In this article, we have learned about fractions. Then we learned about the different rules of how to solve subtracting fractions word problems having like as well as unlike denominators with the help of an example. We became aware of solving, unlike denominators, by taking the help of LCM of the denominators, then multiplying with the numerator and calculating the difference. We also did numerous word problems on fraction subtraction. Kindly solve the given unsolved problems for practice.

FAQs on Subtracting Fractions Word Problems

1. What are the rules for adding fractions?

The basic rule of adding fractions is to first ensure whether the denominators are the same. If the denominators are different, first convert them to equal fractions by taking LCM and then solve the fractions by the usual addition.

2. How to add Improper Fractions?

Improper fractions are added in the same way as proper fractions. Some steps are given below:

If the fractions are the same, add the numerator keeping the same denominator.

To add different fractions, take the lowest common multiple of the denominators, convert them to equivalent fractions, and then add them as equal fractions.

When the addition is complete, and the answer is an improper fraction, convert the fraction to a mixed one and write it in its simplest form.

3. Why are addition and subtraction important?

Addition and subtraction play a very important role in our daily life activities, which involve counting, such as billing at the store, buying groceries, travelling, the speed of a vehicle, checking weight, and so on. It helps us understand situational-based problems. Hence, addition and subtraction are important in our life.

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Adding and Subtracting Fraction Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

16 June 2015

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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[FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

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