How to Find Addition and Subtraction of Fraction Using Like Denominators with Examples - BYJUS

Addition and Subtraction of Fraction Using Like Denominators

Unlike whole numbers, we cannot add two fractions straightaway. First, we must check whether they have the same denominator. If they don’t, we must find an equivalent fraction of one of the fractions in order to make the denominators the same. Learn how to add fractions with the help of some solved examples....Read MoreRead Less

What is Like Denominator?

Like fractions are when two or more fractions have the same denominator.

Example: $$\frac{1}{5},~\frac{3}{5}$$ have a common denominator 5.

How Do We Add Fractions with Like Denominators?

When we are adding fractions with the same denominator, simply add the numerators together and rewrite the sum over the common denominator.

Rule: “To add like fractions, add their numerators and keep the denominator same.”

Example: Find the sum of $$\frac{4}{9},~\frac{5}{9}$$ and $$\frac{1}{9}$$

In the above given fractions, all the fractions have a common denominator. So, we will simply add the numerator taking the denominator as constant.

$$=\frac{4}{9}+\frac{5}{9}+\frac{1}{9}$$     Add the numerator

$$=\frac{4+5+1}{9}=\frac{10}{9}$$

Model: We can use a number line and a box diagram to represent addition of fractions.

• Number Line

The number line is an important linear model for students to use because it reinforces the fact that between two fractions, there is always one more fraction to be found.

Add Fractions Using Number Line for Like Denominator

Create the number line and mention the addend with the dot, then add the part of the other addend from the number line using the curve.

Example: Add the fractions $$\frac{4}{8}+\frac{1}{8}$$ and write the answer.

Draw the number line to represent addend.

Now the addend is $$\frac{1}{8}$$. So, it means that we have to add one part out of 8. Because we’re adding one part, we’ll have to “jump” onwards one step from the maximum.

So, $$\frac{4}{8}+\frac{1}{8}=\frac{5}{8}$$

Add Fractions Using Fraction Strip for Like Denominator

When the denominator of the fraction is the same, we simply add the numerator and represent it in a fraction strip.

As shown in the above image, we have to simply add the numerator.

So, $$\frac{3}{5}+\frac{1}{5}=\frac{4}{5}$$

How do we Subtract Fractions with Like Denominators?

When we are subtracting fractions with the same denominator, simply subtract the numerators with each other and rewrite the difference over the common denominator.

Rule: “To subtract like fractions, subtract their numerators and keep the denominator same.”

Example: Find the difference of $$\frac{13}{9},~\frac{5}{9}$$and $$\frac{2}{9}$$

In the above given fractions, all the fractions have a common denominator. So, we will simply difference the numerator taking the denominator as constant.

$$=\frac{13}{9}-\frac{5}{9}-\frac{2}{9}$$      Add the numerator

$$=\frac{13-5-2}{9}=\frac{6}{9}$$

Model: We can use a number line and a box diagram to represent the difference of fractions.

Subtract Fractions using Fraction Strip

Like Denominator

When the denominator of the fraction is the same, we simply subtract the numerator and represent it in a fraction strip.

As shown in the above image, we have to simply subtract the numerator.

So, $$\frac{5}{8}-\frac{3}{8}=\frac{2}{8}$$

Subtract Fractions using Number Line

Create the number line and mention the minuend with the dot, then subtract the part of the subtrahend from the number line using the curve.

Example: Subtract $$\frac{7}{8}-\frac{2}{8}$$ and write the answer.

Draw the number line to represent minuend.

Now the subtrahend is $$\frac{2}{8}$$. So, it means that we have to subtract two parts out of 8. Because we’re removing two part, we’ll have to “jump” backwards two steps from the minimum.

So, $$\frac{7}{8}-\frac{2}{8}=\frac{5}{8}$$

Solved Example

Example 1: The table shows the favorite sports of 120 students for a sports quiz creation. What fraction of the students like football and baseball as their favorite games.

Each  = 6 students

Solution:

Interpret the above given table:

Baseball: 2 = 2 × 6 = 12 and  = 3

12 + 3 = 15

Football: 4 = 4 × 6 = 24

Write the fraction of the students who likes football and baseball $$=\frac{\text{Number of students}}{\text{Total Students}}$$

Baseball $$=\frac{15}{120}$$ and Football $$=\frac{24}{120}$$

Students like football and baseball as their favourite sports:

$$\frac{15}{120}+\frac{24}{120}$$

= $$\frac{15+24}{120}=\frac{39}{120}$$

Hence, 39 students out of 120 like football and baseball as their favourite sports.

Example 2: Add the fractions $$\frac{1}{8}+\frac{1}{8}$$ and write the answer using the number line.

Solution:

Draw the number line to represent addend.

Now the addend is $$\frac{1}{8}$$. So, it means that we have to add one part out of 8. Because we’re adding one part, we’ll have to “jump” onwards one step from the maximum.

So, $$\frac{1}{8}+\frac{1}{8}=\frac{2}{8}$$

Example 3: Add the fractions $$\frac{1}{6}+\frac{1}{6}$$ and write the answer using the fraction strips.

Solution:

Draw the fraction strip and add the numerator:

As shown in the above image, we have to simply add the numerator.

So, $$\frac{1}{6}+\frac{1}{6}=\frac{2}{6}$$

Example 4: Subtract $$\frac{2}{8}-\frac{1}{8}$$ and write the answer.

Draw the number line to represent minuend.

Now the subtrahend is $$\frac{1}{8}$$. So, it means that we have to subtract one part out of 8. Because we’re removing one part, we’ll have to “jump” backwards one steps from the minimum.

So, $$\frac{2}{8}-\frac{1}{8}=\frac{1}{8}$$

Example 5: Subtract the fractions $$\frac{3}{6}-\frac{1}{6}$$ and write the answer using the fraction strips.

Solution:

Draw the fraction strip and subtract the numerator:

As shown in the above image, we have to simply subtract the numerator.

So, $$\frac{3}{6}-\frac{1}{6}=\frac{2}{6}$$

Example 6: Leo and his friends eat $$\frac{4}{9}$$ slices of pizza. What fraction of its slice is left to eat?

Solution:

There is one whole pizza. So, we have to find $$1-\frac{4}{9}$$

$$1-\frac{4}{9}=\frac{9}{9}-\frac{4}{9}$$

$$=\frac{9-4}{9}$$    Subtract the numerator

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

So, there are $$=\frac{5}{9}$$ slices of pizza are left for them.

Example 7: An office meeting is 1 hour long. All the members arrived after 20 minutes and settled with their laptops in 10 minutes. What fraction of an hour is left for the meeting?

Solution:

The time spent in settlement = 20 + 10 = 30 minutes

We know that 30 minutes $$=\frac{1}{2}$$hour

So, time left for the meeting $$=1-\frac{1}{2}$$

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

$$=\frac{2-1}{2}$$             Subtract the numerator

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

Like fractions are fractions with the same denominators. Add the numerators and write the sum over the denominator to add fractions with like denominators.

Example: $$\frac{3}{10}+\frac{4}{10}=\frac{7}{10}$$

Like fractions are fractions with the same denominators. Subtract the numerators and write the difference over the denominator to subtract fractions with like denominators.

Example: $$\frac{8}{10}-\frac{3}{10}=\frac{5}{10}$$