# how to subtract fractions with different denominators

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## How to Subtract Fractions with Different Denominators

Learn how to subtract fractions with different denominators the easy, the quick trick, and the traditional way.

Basic Math Articles

## How to Subtract Fractions with Different Denominators

**Updated:**07-06-2021

When you want to subtract fractions with different denominators, you have a choice of methods: the easy way, the quick trick, and the traditional way.

The easy way always works, and you should use this method for most of your fraction subtracting needs. The quick trick is a great timesaver, so use it when you can. And as for the traditional way — well, your teacher and other math purists probably prefer you to use it this way.

## Subtract fractions with the easy method

This way of subtracting fractions works in all cases, and it’s easy. Here’s the easy way to subtract fractions that have different denominators:

Cross-multiply the two fractions and subtract the second number from the first to get the numerator of the answer.

For example, suppose you want to subtract 6/7 – 2/5. To get the numerator, cross-multiply the two fractions and then subtract the second number from the first number:

(6 5) – (2 7) = 30 – 14 = 16

After you cross-multiply, be sure to subtract in the correct order. (The first number is the numerator of the first fraction times the denominator of the second.)

Multiply the two denominators together to get the denominator of the answer.

7 5 = 35

Putting the numerator over the denominator gives you your answer.

Here’s another example to work with:

This example puts all the steps together:

With the problem set up like this, you just have to simplify the result:

In this case, you can reduce the fraction:

## Subtract fractions with the quick trick method

The easy way works best when the numerators and denominators are small. When they’re larger, you may be able to take a shortcut.

Before you subtract fractions with different denominators, check the denominators to see whether one is a multiple of the other. If it is, you can use the quick trick:

Increase the terms of the fraction with the smaller denominator so that it has the larger denominator.

For example, suppose you want to find 17/20 – 31/80. If you cross-multiply these fractions, your results are going to be much bigger than you want to work with. But fortunately, 80 is a multiple of 20, so you can use the quick way.

First, increase the terms of 17/20 so that the denominator is 80:

? = 80 ÷ 20 17 = 68

Rewrite the problem, substituting this increased version of the fraction, and subtract.

Here’s the problem as a subtraction of fractions with the same denominator, which is much easier to solve:

In this case, you don’t have to reduce to the lowest terms, although in other problems you may have to.

## Subtract fractions with the traditional method

You should use the traditional way only as a last resort, when the numerator and denominator are too large to use the easy way and when you can’t use the quick trick.

To use the traditional way to subtract fractions with two different denominators, follow these steps:

Find the least common multiple (LCM) of the two denominators.

For example, suppose you want to subtract 7/8 – 11/14. Here’s how to find the LCM of 8 and 14 using the prime factorization method:

8 = 2 2 2 14 = 2 7

In this example, the case where each prime factor appears most often is underlined: 2 appears three times, and 7 appears once. So the LCM of 8 and 14 is

2 2 2 7 = 56

Increase each fraction to higher terms so that the denominator of each equals the LCM.

The denominators of both should be 56:

Substitute these two new fractions for the original ones and subtract.

This time, you don’t need to reduce, because 5 is a prime number and 56 isn’t divisible by 5. In some cases, however, you have to reduce the answer to the lowest terms.

## About This Article

### This article can be found in the category:

Basic Math

Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication

Pre-Algebra Practice Questions: Solving Simple Algebraic Equations

Pre-Algebra Practice Questions: Isolating x in an Equation

Pre-Algebra Practice Questions: Rearranging Equations to Isolate x

Pre-Algebra Practice Questions: Cross-Multiply to Solve Equations

View All Articles From Category

## Subtracting Fractions

Subtracting Fractions

You might like to read Adding Fractions first.

### There are 3 simple steps to subtract fractions

Step 1. Make sure the bottom numbers (the denominators) are the same

Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator.

Step 3. Simplify the fraction (if needed).

Example 1:3

**4**− 1

**4**

**Step 1**. The bottom numbers are already the same. Go straight to step 2.

**Step 2**. Subtract the top numbers and put the answer over the same denominator:

3

**4**− 1

**4**= 3 − 1

**4**= 2

**4**

**Step 3**. Simplify the fraction:

2

**4**= 1

**2**

(If you are unsure of the last step see Equivalent Fractions.)

Example 2:1

**2**− 1

**6**

**Step 1**. The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we

**can't**subtract them like this:

1

**2**− 1

**6**= ?

To make the bottom numbers the same, multiply the top and bottom of the first fraction (1/2) by **3** like this:

× 3 1

**2**= 3

**6**

× 3

And now our question looks like this:

3

**6**− 1

**6**

The bottom numbers (the denominators) are the same, so we can go to step 2.

**Step 2**. Subtract the top numbers and put the answer over the same denominator:

3

**6**− 1

**6**= 3 − 1

**6**= 2

**6**

In picture form it looks like this:

3

**6**− 1

**6**= 2

**6**

**Step 3**. Simplify the fraction:

2

**6**= 1

**3**

### With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

### Play with it!

Try Subtracting Fractions Illustrated.

## Subtracting Mixed Fractions

I have a special page on Adding and Subtracting Mixed Fractions.

## Making the Denominators the Same

In the previous example it was easy to make the denominators the same, but it can be harder ... so you may need to use either the

Common Denominator Method, or the

Least Common Denominator Method

They both work, use which one you prefer!

Example: CupcakesYou want to sell cupcakes at a market:

You get paid 2

**5**of total sales

But you have to pay 1

**4**of total sales for the stall

How much do you get?

We need to subtract 1

**4**from 2

**5**

2

**5**− 1

**4**= ?

**?**

**First**make the bottom numbers (the denominators) the same.

Multiply top and bottom of 2/5 by **4**:

2 × 4

**5 × 4**− 1

**4**= ?

**?**

And multiply top and bottom of 1/4 by **5**:

2 × 4

**5 × 4**− 1 × 5

**4 × 5**= ?

**?**

**Now**do the calculations:

8

**20**− 5

**20**= 8 − 5

**20**= 3

**20**

Answer: you get to keep** 3**

**20 **of total sales.

Worksheets Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10

Introduction to Fractions

Subtracting Fractions Illustrated

Simplifying Fractions

Equivalent Fractions

Adding Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions Fractions Index

## Subtracting fractions with unlike denominators (video)

Sal subtracts fractions like 4/3 and 1/5.

Current time:0:00Total duration:5:01

Adding and subtracting fractions with unlike denominators

## Subtracting fractions with unlike denominators

Sal subtracts fractions like 4/3 and 1/5.

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## Adding and subtracting fractions with unlike denominators

Adding fractions with unlike denominators introduction

Adding fractions with unlike denominators

Practice: Add fractions with unlike denominators

Subtracting fractions with unlike denominators introduction

Subtracting fractions with unlike denominators

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Practice: Subtracting fractions with unlike denominators

Adding and subtracting 3 fractions

Solving for the missing fraction

Practice: Add and subtract fractions

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Adding and subtracting mixed numbers with unlike denominators

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## Want to join the conversation?

Log in Trinidad Melanie 6 years ago

Posted 6 years ago. Direct link to Trinidad Melanie's post “what if they are the sam...”

what if they are the same denominaters

• owokids 5 years ago

Posted 5 years ago. Direct link to owokids's post “If the denominators are t...”

If the denominators are the same , you leave the denominators the same and add or subtract the numerators. Make sure you don't add or subtract the denominators.

Tatum Brewer 4 years ago

Posted 4 years ago. Direct link to Tatum Brewer's post “What do i do when i have ...”

What do i do when i have this?

14/6

The numerator is bigger than the denominator.

• danebird a year ago

Posted a year ago. Direct link to danebird's post “The answer would be 2 2/6...”

The answer would be 2 2/6 because 6 goes into 14 2 times and 2 would be left and that turns into the numerator, and the denominator would stay the same

Blake Mcgill 4 years ago

Posted 4 years ago. Direct link to Blake Mcgill's post “how do you subtract 8/2 -...”

how do you subtract 8/2 - 7/12

• Wesley Ochocki 4 years ago

Posted 4 years ago. Direct link to Wesley Ochocki's post “create common denominator...”

create common denominators so set 8/2 to 48/12 (6 x 2=12, 8 x 6=48) then subtract 48 by 7 to get 41 and place that back over 12 to get 41/12

ic070109 3 years ago

Posted 3 years ago. Direct link to ic070109's post “how do you multiply or di...”

how do you multiply or divide with unlike denominators

• Shriya 3 years ago

Posted 3 years ago. Direct link to Shriya's post “When multiplying and divi...”

When multiplying and dividing fractions, there is no need for a common denominator.

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators.

Ex. 1/5 x 1/4 = 1/20

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

Ex. 2/5 ÷ 2/3 = 2/5 x 3/2 = 6/10

Here are some links that might help:

https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions/multiply-fractions/v/multiplying-a-fraction-by-a-fraction

https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions/dividing-fractions/v/dividing-fractions-example

Good Luck! gabrielle.costa 4 years ago

Posted 4 years ago. Direct link to gabrielle.costa's post “what if there is 2 diffre...”

what if there is 2 diffrent denomanonater

• Katherine lau 4 years ago

Posted 4 years ago. Direct link to Katherine lau's post “You will have to find a m...”

You will have to find a multiple that both denominators have. Then, multiply the numerator by the number you multiplied the denominator to get the common multiple.

For example: 5/9 - 6/5

You will need to find a common multiple that 9 and 5 both have.

9: 9, 18, 27, 36, 45, 54...

5: 5, 10, 15, 20, 25, 30, 35, 45, 50...

In this case 45 is the common multiple. Then, you would have to multiply the numerators by the number you multiplied their denominator to get the common multiple. Since 9 times 5 equals 45, the 5 in 5/9 needs to be multiplied by 5 and the 6 in 6/5 would need to be multiplied by 9.

So, 5/9 becomes 25/45 and 6/5 becomes 54/45.

Therefore, 25/45 - 54/45 = -29/45

Hope this helped :) jonathan.cano2 3 years ago

Posted 3 years ago. Direct link to jonathan.cano2's post “what if there numerators ...”

what if there numerators are bigger than there denominators

• GalaxyQueen735 3 years ago

Posted 3 years ago. Direct link to GalaxyQueen735's post “then you turn the fractio...”

then you turn the fraction into a mixed number

51110 a year ago

Posted a year ago. Direct link to 51110's post “how do I subtract mixed f...”

how do I subtract mixed fraction where only one fraction is mixed

• Kevin L. a year ago

Posted a year ago. Direct link to Kevin L.'s post “You turn both fractions i...”

You turn both fractions into improper fractions, next you find a like denominator, then you subtract.

Guys, does anyone know the answer?