How do you add or subtract fractions with unlike denominators

Are you trying to plow through that fractions unit, but feeling frustrated because you still can't figure out the concept of subtracting fractions with unlike denominators?

If so, you are not alone. My statistics show that more people seek help with fractions than any other math concept.

The good news is, you can wave goodbye to your frustrations!

I am going to walk you step-by-step through several examples and by the end you will feel confident with subtracting fractions with different denominators. I promise!

Let's take a look at Example 1.

Example 1 - Subtracting Fractions with Unlike Denominators

Not too bad, right? In that example one of the fractions happened to have a denominator that was the least common denominator.

Notice how once the denominators are the same, all we need to do is subtract the numerators.

Steps for Subtracting Fractions with Unlike Denominators

1. Identify the least common denominator by finding the least common multiple for the denominators.

2. Write equivalent fractions (making sure that each equivalent fraction contains the least common denominator (LCM))

3. Subtract the numerators of the equivalent fractions that you wrote in step 2. (The denominators should now be the same.)

4. Simplify if necessary.

Jot those 4 steps down if you are having trouble remembering the steps for subtracting fractions.

Let's take a look at another example. This time, neither denominator is the least common denominator. I will also demonstrate how to subtract fractions that are written vertically.

Example 2 - Subtracting Fractions Vertically

Will you work with integers (positive and negative numbers) when working with fractions?

Yes, absolutely! Let's take a look!

Example 3 - Can you have a negative fraction?

So, do you feel more confident with subtracting fractions with different denominators? I hope so! You may be ready to start adding or subtracting mixed numbers.

1. Home
>
2. Fractions
>
3. Subtracting Fractions

Need More Help With Your Algebra Studies?

Get access to hundreds of video examples and practice problems with your subscription! 

Click here for more information on our affordable subscription options.

Not ready to subscribe?  Register for our FREE Pre-Algebra Refresher course.

Adding and Subtracting Fractions with Different Denominators

Step 1: Identify the denominator of the fractions that are being added or subtracted.

Step 2: Find the least common multiple (LCM) of the denominators. To find the LCM of the denominators, find the multiples of each denominator. Then, look for the lowest multiple that is common to both denominators. That will be the least common multiple.

Step 3: Rewrite each fraction to its equivalent fraction with a denominator equal to the least common multiple(LCM).

Step 4: Add or subtract the equivalent fractions obtained in step 3 to get the final answer. Add or subtract the numerator as required in the problem. The denominator of the answer will be the same as the denominator of the fractions that are being added or subtracted.

Adding and Subtracting Fractions with Different Denominators Vocabulary

Fractions: Fractions represent a part of the whole. They can be written as {eq}\frac{p}{q} {/eq}, where {eq}q\neq 0 {/eq}. The number {eq}p {/eq} is the numerator in the fraction, and the number {eq}q {/eq} is the denominator in the fraction.

Equivalent fraction: Equivalent fraction to a given fraction is a fraction with a different numerator and a different denominator but it has the same value as the given fraction.

We will take a look at two examples to get a clear understanding of the concept of adding or subtracting fractions with different denominators. The first example will show the addition of fractions with different denominators while the second example will show the subtraction of fractions with different denominators.

Adding and Subtracting Fractions with Different Denominators: Adding the Fractions Example

Find the sum: {eq}\frac{3}{5} + \frac{6}{7} {/eq}

Step 1: Identify the denominator of the fractions that are being added or subtracted.

The denominators of the fractions that are being added are 5 and 7.

Step 2: Find the least common multiple (LCM) of the denominators.

List the multiples of 5 and 7 and look for the lowest multiple that is common in the lists.

Multiples of 5 are: 5, 10, 15, 20, 15, 30, 35, 40

Multiples of 7 are: 7, 14, 21, 28, 35

The lowest multiple that is common in the list is 35.

Therefore, the LCM is 35.

Step 3: Rewrite each fraction to its equivalent fraction with a denominator equal to the least common multiple(LCM).

Rewrite {eq}\frac{3}{5} {/eq} to its equivalent fraction with a denominator of 35.

Think of a number which when multiplied by 5 gives 35.

{eq}5\times{7} = 35 {/eq}

We multiply the numerator and the denominator by 7 to get an equivalent fraction.

{eq}\frac{3\times{7}}{5\times{7}} = \frac{21}{35} {/eq}

Rewrite {eq}\frac{6}{7} {/eq} to its equivalent fraction with a denominator of 35

Think of a number which when multiplied by 7 gives 35.

{eq}7\times{5} = 35 {/eq}

We multiply the numerator and the denominator by 5 to get an equivalent fraction.

{eq}\frac{6\times{5}}{7\times{5}} = \frac{30}{35} {/eq}

Step 4: Add or subtract the equivalent fractions obtained in step 3 to get the final answer.

{eq}\frac{21}{35} + \frac{30}{35} = \frac{51}{35} {/eq}

Adding and Subtracting Fractions with Different Denominators: Subtracting the Fractions Example

Find the difference: {eq}\frac{2}{5} - \frac{3}{8} {/eq}

Step 1: Identify the denominator of the fractions that are being added or subtracted.

The denominators of the fractions that are being subtracted are 5 and 8.

Step 2: Find the least common multiple (LCM) of the denominators.

List the multiples of 5 and 8 and look for the lowest multiple that is common in the lists.

Multiples of 5 are: 5, 10, 15, 20, 15, 30, 35, 40

Multiples of 8 are: 8, 16, 24, 32, 40

The lowest multiple that is common in the list is 40

Therefore, the LCM is 40

Step 3: Rewrite each fraction to its equivalent fraction with a denominator equal to the least common multiple (LCM).

Rewrite {eq}\frac{2}{5} {/eq} to its equivalent fraction with a denominator of 40.

Think of a number that when multiplied by 5 gives 40.

{eq}5\times{8} = 40 {/eq}

We multiply the numerator and the denominator by 8 to get an equivalent fraction.

{eq}\frac{2\times{8}}{5\times{8}} = \frac{16}{40} {/eq}

Rewrite {eq}\frac{3}{8} {/eq} to its equivalent fraction with a denominator of 40.

We multiply the numerator and the denominator by 5 to get an equivalent fraction.

{eq}\frac{3\times{5}}{8\times{5}} = \frac{15}{40} {/eq}

Step 4: Add or subtract the equivalent fractions obtained in step 3 to get the final answer.

{eq}\frac{16}{40} - \frac{15}{40} = \frac{1}{40} {/eq}

Get access to thousands of practice questions and explanations!

How do you add fractions with unlike denominators step by step?

How do you subtract unlike fractions step by step?