**Addition of Unlike Fractions:** If the denominators or bottom number of the fractions are not the same then it is known as, unlike fraction. Here you can gain more knowledge about adding fractions with unlike denominators. In order to make the denominators common, we have to find the least common multiples of the denominators.

Students must know about the fractions before they start adding the like or unlike fractions. The Addition of Unlike fractions is somewhat tricky, but you can make it easy by making the denominators equal. Read the entire article to know how to add unlike fractions, the addition of unlike fractions questions.

**Do Refer:**

- Addition of Like Fractions
- Addition of Fractions having the Same Denominator
- Conversion of Fractions into Fractions having Same Denominator

## What is a Fraction?

In maths, A fraction is a numerical quantity that is not a whole number. Fractions will divide the whole number into equal parts. For example, an apple is divided into two parts, then each part is represented by \(\frac{1}{2}\).

### How to Solve Addition of Unlike Fractions?

There are some rules to follow for adding unlike fractions. They are given below.

1. First check the denominators or bottom numbers of two fractions.

2. Find the Least Common Multiple for the denominators.

3. Multiply the numerator and denominator in order to get the like fractions.

4. Solve the sum of two fractions.

5. Simply the fractions if needed.

### Adding Fractions with Unlike Denominators Examples

Let us consider some examples to know briefly about the Addition of Fractions Unlike Denominators.

**Question 1.**

Add \(\frac{2}{3}\) and \(\frac{1}{5}\) having unlike fractions.

**Solution:**

Given, the fractions \(\frac{2}{3}\) and \(\frac{1}{5}\)

Step 1: First check the denominators or bottom numbers of two fractions

Here the denominators of the given fractions are not same.

Step 2: Find the Least Common Multiple for the denominators.

The multiples of 3 are 3, 6, 9, 12, **15**…

The multiples of 5 are 5, 10, **15**, 20, ….

Thus the L.C.M. of 3 and 5 is 15.

Step 3: Multiply the numerator and denominator in order to get the like fractions.

\(\frac{2}{3}\) × \(\frac{5}{5}\) + \(\frac{1}{5}\) × \(\frac{3}{3}\)

= \(\frac{10}{15}\) + \(\frac{3}{15}\) = \(\frac{13}{15}\)

Simplification of the fraction is not possible here.

Therefore the sum of \(\frac{2}{3}\) and \(\frac{1}{5}\) having unlike fractions is \(\frac{13}{15}\).

**Question 2.**

Add \(\frac{2}{7}\) and \(\frac{1}{3}\) having unlike fractions.

**Solution:**

Given, the fractions \(\frac{2}{7}\) and \(\frac{1}{3}\)

Step 1: First check the denominators or bottom numbers of two fractions

Here the denominators of the given fractions are not same.

Step 2: Find the Least Common Multiple for the denominators.

The multiples of 3 are 3, 6, 9, 12, 15, 18, **21**…

The multiples of 7 are 7, 14, **21**, 28 ….

Thus the L.C.M. of 3 and 7 is 21.

Step 3: Multiply the numerator and denominator in order to get the like fractions.

\(\frac{2}{7}\) × \(\frac{3}{3}\) + \(\frac{1}{3}\) × \(\frac{7}{7}\)

= \(\frac{6}{21}\) + \(\frac{7}{21}\) = \(\frac{13}{21}\)

Simplification of the fraction is not possible here.

Therefore the sum of \(\frac{2}{7}\) and \(\frac{1}{3}\) having unlike fractions is \(\frac{13}{21}\)

**Question 3.**

Add \(\frac{2}{6}\) and \(\frac{2}{5}\) having unlike fractions.

**Solution:**

Given, the fractions \(\frac{2}{6}\) and \(\frac{2}{5}\)

Step 1: First check the denominators or bottom numbers of two fractions

Here the denominators of the given fractions are not same.

Step 2: Find the Least Common Multiple for the denominators.

The multiples of 6 are 6, 12, 18, 24, 30….

The multiples of 5 are 5, 10, 15, 20, 25, 30 ….

Thus the L.C.M. of 6 and 5 is 30.

Step 3: Multiply the numerator and denominator in order to get the like fractions.

\(\frac{2}{6}\) × \(\frac{5}{5}\) + \(\frac{2}{5}\) × \(\frac{6}{6}\)

= \(\frac{10}{30}\) + \(\frac{12}{30}\) = \(\frac{22}{30}\)

Simplification of the fraction is possible here.

\(\frac{22}{30}\) = \(\frac{11}{15}\)

Therefore the sum of \(\frac{2}{6}\) and \(\frac{2}{5}\) having unlike fractions is \(\frac{11}{15}\)

**Question 4.**

Add \(\frac{3}{8}\) and \(\frac{9}{10}\) having unlike fractions.

**Solution:**

Given, the fractions \(\frac{3}{8}\) and \(\frac{9}{10}\)

Step 1: First check the denominators or bottom numbers of two fractions

Here the denominators of the given fractions are not same.

Step 2: Find the Least Common Multiple for the denominators.

The multiples of 8 are 8, 16, 24, 32, 40,…

The multiples of 10 are 10, 20,30, 40 ….

Thus the L.C.M. of 8 and 10 is 40.

Step 3: Multiply the numerator and denominator in order to get the like fractions.

\(\frac{3}{8}\) × \(\frac{5}{5}\) + \(\frac{9}{10}\) × \(\frac{4}{4}\)

= \(\frac{15}{40}\) + \(\frac{36}{40}\) = \(\frac{51}{40}\)

Simplification of the fraction is not possible here.

Therefore the sum of \(\frac{3}{8}\) and \(\frac{9}{10}\) having unlike fractions is \(\frac{51}{40}\)

**Question 5.**

Add \(\frac{5}{7}\) and \(\frac{3}{5}\) having unlike fractions.

**Solution:**

Given, the fractions \(\frac{5}{7}\) and \(\frac{3}{5}\)

Step 1: First check the denominators or bottom numbers of two fractions

Here the denominators of the given fractions are not same.

Step 2: Find the Least Common Multiple for the denominators.

The multiples of 7 are 7, 14, 21, 28, 35,…

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, ….

Thus the L.C.M. of 7 and 5 is 35.

Step 3: Multiply the numerator and denominator in order to get the like fractions.

\(\frac{5}{7}\) × \(\frac{5}{5}\) + \(\frac{3}{5}\) × \(\frac{7}{7}\)

= \(\frac{25}{35}\) + \(\frac{21}{35}\) = \(\frac{46}{35}\)

Simplification of the fraction is not possible here.

Therefore the sum of \(\frac{5}{7}\) and \(\frac{3}{5}\) having unlike fractions is \(\frac{46}{35}\)

## FAQs on Adding Unlike Fractions

**1. What is an unlike fraction and write an example?**

Unlike fractions are the fractions that have different denominators.

**Example:** \(\frac{2}{6}\) and \(\frac{4}{5}\) are the fractions that have different denominators.

**2. How do you add unlike fractions?**

You can add the unlike fractions by finding the least common multiples of the given denominators. After that make the denominators equal and then add the numerator and write the common denominator.

**3. Give an example of the addition of unlike fractions.**

Add the fractions \(\frac{2}{3}\) and \(\frac{1}{2}\) having unlike denominators.

**Solution:**

First find the least common multiples of 2 and 3.

The multiples of 2 are 2, 4, **6**, 8..

The multiples of 3 are 3, **6**, 9, 12…

Thus the L.C.M. of 2 and 3 is 6.

\(\frac{2}{3}\) × \(\frac{2}{2}\) + \(\frac{1}{2}\) × \(\frac{3}{3}\)

= \(\frac{4}{6}\) + \(\frac{3}{6}\)

Now the denominators of both the fractions are the same.

\(\frac{4+3}{6}\) = \(\frac{7}{6}\)

Thus the sum of fractions \(\frac{2}{3}\) and \(\frac{1}{2}\) is \(\frac{7}{6}\).