# Subtract Fractions with Like Denominators – Step-by-step

Fractions that have the same denominators are called like fractions. We can subtract these types of fractions by writing them with a single denominator. Then, we subtract the numerators, and we will get the result. Finally, we can simplify the final fraction if possible.

Here, we will learn how to subtract like fractions step by step. Then we will use those steps to solve some practice problems.

##### ARITHMETIC

Relevant for

Learning to subtract fractions with the same denominator.

See steps

##### ARITHMETIC

Relevant for

Learning to subtract fractions with the same denominator.

See steps

## Steps to subtract like fractions

Like fractions are fractions that have the same denominator. To subtract these types of fractions, we can follow the following steps:

Step 1: Make sure the denominator of the fractions is the same.

Note: The denominator is the number at the bottom of the fraction, and the numerator is the number at the top of the fraction.

Step 2: Combine the fractions into a single denominator. Since the denominator is the same, we can write the fractions in a single denominator.

Step 3: Subtract the numerators of the fraction obtained in step 2.

Step 4: Simplify the final result if possible.

Using these steps, we can solve the subtraction of any number of fractions. In the following examples, you can look at the steps in detail.

## Subtract like fractions – Examples with answers

The following examples are solved using the steps for solving subtraction of like fractions seen above. Try to solve the problems yourself before looking at the solution.

### EXAMPLE 1

Find the result of the subtraction $latex \frac{2}{3}-\frac{1}{3}$.

Step 1: The denominators of both fractions are equal to 3, so we have like fractions.

Step 2: Combining the fractions, we have:

$$\frac{2}{3}-\frac{1}{3}$$

$$=\frac{2-1}{3}$$

Step 3: Subtracting the numerators, we have:

$$=\frac{2-1}{3}$$

$$=\frac{1}{3}$$

Step 4: The fraction is now simplified.

### EXAMPLE 2

Solve the subtraction of like fractions $latex \frac{4}{5}-\frac{2}{5}$.

Step 1: We have like fractions because the denominators are the same.

Step 2: Writing the fractions as one, we have:

$$\frac{4}{5}-\frac{2}{5}$$

$$=\frac{4-2}{5}$$

Step 3: Subtracting the numerators, we have:

$$=\frac{4-2}{5}$$

$$=\frac{2}{5}$$

Step 4: The fraction is now simplified.

### EXAMPLE 3

Solve the subtraction of fractions $latex \frac{7}{5}-\frac{4}{5}$.

Step 1: We have like fractions because both denominators are equal to 5.

Step 2: Writing the fractions with a single denominator, we have:

$$\frac{7}{5}-\frac{4}{5}$$

$$=\frac{7-4}{5}$$

Step 3: Subtracting the numerators, we have:

$$=\frac{7-4}{5}$$

$$=\frac{3}{5}$$

Step 4: The fraction is now simplified.

### EXAMPLE 4

Solve the subtraction of fractions $latex \frac{11}{9}-\frac{4}{9}-\frac{2}{9}$.

Step 1: All three denominators are the same, so the fractions are like.

Step 2: Writing the fractions with a single denominator, we have:

$$\frac{11}{9}-\frac{4}{9}-\frac{2}{9}$$

$$=\frac{11-4-2}{9}$$

Step 3: Subtracting the numerators, we have:

$$=\frac{11-4-2}{9}$$

$$=\frac{5}{9}$$

Step 4: The fraction is now simplified.

### EXAMPLE 5

Find the result of the subtraction $latex \frac{7}{5}-\frac{2}{10}-\frac{3}{5}$.

Step 1: In this case, the fractions do not appear to be like. However, we can simplify the second fraction as follows:

$$\frac{7}{5}-\frac{2}{10}-\frac{3}{5}$$

$$=\frac{7}{5}-\frac{1}{5}-\frac{3}{5}$$

Step 2: Using a single denominator, we have:

$$\frac{7}{5}-\frac{1}{5}-\frac{3}{5}$$

$$=\frac{7-1-3}{5}$$

Step 3: Subtracting the numerators, we have:

$$=\frac{7-1-3}{5}$$

$$=\frac{3}{5}$$

Step 4: The fraction is now simplified.

### EXAMPLE 6

Find the result of $latex \frac{18}{11}-\frac{9}{33}-\frac{4}{11}$.

Step 1: We can simplify the second fraction to obtain like denominators:

$$\frac{18}{11}-\frac{9}{33}-\frac{4}{11}$$

$$=\frac{18}{11}-\frac{3}{11}-\frac{4}{11}$$

Step 2: Using a single denominator, we have:

$$\frac{18}{11}-\frac{3}{11}-\frac{4}{11}$$

$$=\frac{18-3-4}{11}$$

Step 3: Subtracting the numerators, we have:

$$=\frac{18-3-4}{11}$$

$$=\frac{11}{11}$$

Step 4: Simplifying, we have:

$$=1$$

## Subtraction of like fractions – Practice problems

Practice everything you learned about subtracting like fractions by solving the following problems.

#### Solve the addition $latex \frac{6}{7}-\frac{4}{14}-\frac{2}{7}$  