Subtracting Fractions with Like Denominators

Performing fraction operations is different from performing basic operations on whole numbers. Fractions require you to consider both the numerator and denominator when making calculations. Fortunately, when subtracting fractions with like denominators, the numerator is your only concern. Let''s look at the steps you''ll take to make these calculations.

How to subtract fractions with like denominators

Whenever you subtract fractions, you always want to make sure that your denominators are the same. Fractions with the same denominators are called like fractions.

In order to subtract fractions with like denominators, we''ll first subtract the numerators, and then write the difference over the denominator.

Let''s look at an example:

Find:

5/7 - 4/7

As you can see, the denominators are the same, so we''ll simply subtract the numerators.

(5 − 4)/7 = 1/7

Here is a visual representation:

Let''s try another example:

Find:

4/5 − 2/5

The denominators are the same, so we''ll go ahead and subtract the numerators.

(4 − 2)/5

= 2/5

How to reduce fractions not in lowest terms

When subtracting fractions, you might get answers that are not in lowest terms. When a fraction is in lowest terms, the numerator and denominator are relatively prime -- or have no common factors other than 1.

If you get an answer that is not in lowest terms, you''ll want to reduce the fraction. Here''s how to do it:

First, let''s find:

8/9 - 2/9

The denominators are the same, so let''s subtract the numerators.

(8 - 2)/9 = 6/9

Now, we have a resulting fraction that is not in lowest terms. To put it in lowest terms, we''ll divide both the numerator and denominator by the greatest common factor, in this case 3.

6/9 = (6 ÷ 3)/(9 ÷ 3) = 2/3

Therefore,

6/9

in lowest terms is

2/3

Practice questions on subtracting fractions with like denominators

a. Find:

15/7 - 11/7.

(15 - 11)/7

Answer:

4/7

b. Find:

3/4 - 2/4.

3 - 2/4

Answer:

1/4

c. Find:

11/9 - 6/9.

(11 - 6)/9

Answer:

5/9

d. Put

9/12

in lowest terms.

The greatest common factor is 3.

(9 ÷ 3)/(12 ÷ 3)

Answer:

3/4

e. Put

5/15

in lowest terms.

The greatest common factor is 5.

(5 ÷ 5)/(15 ÷ 5)

Answer:

1/5

f. Find

10/12 - 2/12

and put in lowest terms.

(10 - 2)/12

= 8/12

The greatest common factor is 4.

(8 ÷ 4)/(12 ÷ 4)

= 2/3

Topics related to the Subtracting Fractions with Like Denominators

Least Common Denominators (LCDs)

Subtracting Fractions with Unlike Denominators

Combining Like Terms

Flashcards covering the Subtracting Fractions with Like Denominators

Basic Arithmetic Flashcards

ACCUPLACER Arithmetic Flashcards

Practice tests covering the Subtracting Fractions with Like Denominators

Basic Arithmetic Diagnostic Tests

Better understand how to subtract fractions with like denominators

When first learning to subtract fractions with like denominators, it can be tough to remember every step in the process. For example, your student might remember to make sure the denominators are the same, but forget not to subtract the denominators. If your student is struggling with this concept or would like help with assignments or test preparations, tutoring can make a big difference. Find out the many ways a private instructor can use their expertise to help your student excel by contacting the Educational Directors at Varsity Tutors today.