## How to Add and Subtract Fractions

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Fractions are generally used to define any whole number into equal parts. While writing a fraction, there are two numbers involved. The number at the top is called the **numerator**, while that at the bottom is called a **denominator**. There are three types of fractions. They are:

**Proper Fractions**: In proper fractions, the denominator is greater than the numerator. For ex: \( \frac{3}{4} \ , \ \frac{1}{3} \)**Improper Fraction**: As the name suggests, these fractions are “top-heavy” or the numerator is greater than the denominator. For ex: \( \frac{7}{8} \ , \ \frac{5}{2} \)**Mixed-Fraction**: Mixed fractions are another type of improper fractions where there is a whole number as well as a fraction part. For ex: \( 1\frac{1}{3} \ , \ 2\frac{3}{7} \)

To, add or subtract fractions, we need to follow certain criterions. First, we need to look for like and un-like fractions.

**Addition & Subtraction with Like Fractions**

Two fractions whose denominators are same are called like fractions. So, to add or subtract, just perform addition/subtraction between the numerator part, and then write the answer over the common denominator.

Example \( \frac{a}{b} + \frac{c}{b} = \frac{a+c}{b} \)

So, for example, \( \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \)

**Addition and Subtraction with Unlike Fractions**

For un-like fractions or fractions with different denominators, we will perform the operation like this.

Example \( \frac{a}{b} + \frac{c}{d} = \frac{ad+cb}{bd} \)

Also, \( \frac{a}{b} - \frac{c}{d} = \frac{ad-cb}{bd} \)

So, for example, \( \frac{2}{5} - \frac{1}{6} = \frac{12-5}{30} = \frac{7}{30} \)

finally, you may have a fraction that can be reduced to a simpler fraction. it's always best to reduce simplest form when you can. Learn more

### Related Topics

How to Simplify Fractions

How to Multiply and Divide Fractions

How to Convert Between Fractions, Decimals, and Mixed Numbers

How to Convert Between Percent, Fractions, and Decimals

### Exercises for Add or Subtract Fractions

**1)** \({7 \over 4} \ + \ {5 \over 6} = \)

**2)**\({8 \over 10} \ + \ {2 \over 3} = \)

**3)**\({9 \over 8} \ + \ {8 \over 2} = \)

**4)**\({5 \over 3} \ - \ {3 \over 5} = \)

**5)**\({6 \over 3} \ - \ {8 \over 8} = \)

**6)**\({5 \over 1} \ - \ {5 \over 4} = \)

**7)**\({3 \over 2} \ - \ {7 \over 8} = \)

**8)**\({9 \over 3} \ - \ {3 \over 5} = \)

**9)**\({7 \over 11} \ + \ {16 \over 17} = \)

**10)**\({8 \over 9} \ + \ {15 \over 10} = \)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({7 \over 4} \ + \ {5 \over 6} = \)\( \ {7 \times 6 \ + \ 5 \times 4 \over 4\times6} =\)\({62 \over 24}\)

Then, simplify the result. \({62 \over 24} = {31 \over 12}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({8 \over 10} \ + \ {2 \over 3} = \)\( \ {8 \times 3 \ + \ 2 \times 10 \over 10\times3} =\) = \( {44 \over 30}\)

Then, simplify the result. \({44 \over 30} = {22 \over 15}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({9 \over 8} \ + \ {8 \over 2} = \)\( \ {9 \times 2 \ + \ 8 \times 8 \over 8\times2} =\)\({82 \over 16}\)

Then, simplify the result. \({82 \over 16} = {41 \over 8}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({5 \over 3} \ - \ {3 \over 5} = \)\( \ {5 \times 5 \ - \ 5 \times 3 \over 3\times5} = \)\({15 \over 10}\)

Then, simplify the result. \({2 \over 3} = 1\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({6 \over 3} \ - \ {8 \over 8} = \)\( \ {6 \times 8 \ - \ 8 \times 3 \over 3\times8} = \)\({24 \over 24}\)

Then, simplify the result. \({15 \over 15} = 1\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({5 \over 1} \ - \ {5 \over 4} = \)\( \ {5 \times 4 \ - \ 5 \times 1 \over 1\times4} = \)\({15 \over 4}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({3 \over 2} \ - \ {7 \over 8} = \)\( \ {3 \times 8 \ - \ 7 \times 2 \over 2\times8} = \)\({10 \over 16}\)

Then, simplify the result. \({10 \over 16} = { 5 \over 8}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction.\({9 \over 3} \ - \ {3 \over 5} = \)\( \ {9 \times 5 \ - \ 3 \times 3 \over 3\times5} = \)\({36 \over 15}\)

Then, simplify the result. \({36 \over 15} = { 12 \over 5}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({7 \over 11} \ + \ {16 \over 17} = \)\( \ {7 \times 17 \ + \ 16 \times 11 \over 11\times17} =\)\({295 \over 187}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({8 \over 9} \ + \ {15 \over 10} = \)\( \ {8 \times 10 \ + \ 15 \times 9 \over 9\times10} = \)\({215 \over 90}\)

Then, simplify the result. \({215 \over 90} = { 43 \over 18} \)

## Add and Subtract Fractions Quiz

### More Math Articles

- How to Simplify Fractions
- How to Add and Subtract Fractions
- How to Multiply Mixed Numbers
- How to Compare Decimals
- How to Multiply and Divide Fractions
- How to Add Mixed Numbers
- How to Round Off Decimals
- How to Subtract Mixed Numbers
- How to Divide Mixed Numbers
- How to Add or Subtract Decimals
- How to Multiply or Divide Decimals
- How to Convert between Fractions, Decimals and Mixed Numbers
- How to Factor Numbers
- How to Find the Greatest Common Factor (GCF)
- How to Find the Least Common Multiple (LCM)
- What are the Divisibility Rules