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

Free printable Worksheets

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

Answers

1)\({7 \over 4} \ + \ {5 \over 6} = \)\( \ \color{red}{{7 \times 6 \ + \ 5 \times 4 \over 4\times6} = } \)\({\color{red}{62 \over 24}}\)\(\color{red}{ = {62 \div 2 \over 24 \div 2} = {31 \over 12}}\)

GCF(62,24) = 2

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. \({62 \over 24} = {31 \over 12}\)

2)\({8 \over 10} \ + \ {2 \over 3} = \)\( \ \color{red}{{8 \times 3 \ + \ 2 \times 10 \over 10 \times 3} = } \) \({\color{red}{44 \over 30}}\)\(\color{red}{ = {44 \div 2 \over 30 \div 2} = {22 \over 15}} \)

GCF(44,30) = 2

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. \({44 \over 30} = {22 \over 15}\)

3)\({9 \over 8} \ + \ {8 \over 2} = \)\( \ \color{red}{{9 \times 2 \ + \ 8 \times 8 \over 8\times2} = } \) \({\color{red}{82 \over 16}}\)\(\color{red}{ = {82 \div 2 \over 16 \div 2} = {41 \over 8}} \)

GCF(82,16) = 2

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. \({82 \over 16} = {41 \over 8}\)

4)\({5 \over 3} \ - \ {3 \over 5} = \)\( \ \color{red}{{5 \times 5 \ - \ 5 \times 3 \over 3\times5} = } \) \({\color{red}{10 \over 15}}\)\(\color{red}{ = {10 \div 5 \over 15 \div 5} = {2 \over 3}} \)

GCF(10,15) =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. \({5 \over 3} \ - \ {3 \over 5} = \)\( \ {5 \times 5 \ - \ 5 \times 3 \over 3\times5} = \)\({15 \over 10}\)
Then, simplify the result. \({2 \over 3} = 1\)

5)\({6 \over 3} \ - \ {8 \over 8} = \)\( \ \color{red}{{6 \times 8 \ - \ 8 \times 3 \over 3\times8} = } \) \({\color{red}{24 \over 24}}\)\(\color{red}{ = 1}\)

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. \({15 \over 15} = 1\)

6)\({5 \over 1} \ - \ {5 \over 4} = \)\( \ \color{red}{{5 \times 4 \ - \ 5 \times 1 \over 1\times4} = } \) \({\color{red}{15 \over 4}}\)

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. \({5 \over 1} \ - \ {5 \over 4} = \)\( \ {5 \times 4 \ - \ 5 \times 1 \over 1\times4} = \)\({15 \over 4}\)

7)\({3 \over 2} \ - \ {7 \over 8} = \)\( \ \color{red}{{3 \times 8 \ - \ 7 \times 2 \over 2\times8} = } \) \({\color{red}{10 \over 16}}\)\(\color{red}{ = {10 \div 2 \over 16 \div 2} = {5 \over 8}}\)

GCF(10,16) = 2

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. \({10 \over 16} = { 5 \over 8}\)

8)\({9 \over 3} \ - \ {3 \over 5} = \)\( \ \color{red}{{9 \times 5 \ - \ 3 \times 3 \over 3\times5} = } \) \({\color{red}{36 \over 15}}\)\(\color{red}{ = {36 \div 3 \over 15 \div 3} = {12 \over 5}}\)

GCF(36,15) = 3

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. \({36 \over 15} = { 12 \over 5}\)

9)\({7 \over 11} \ + \ {16 \over 17} = \)\( \ \color{red}{{7 \times 17 \ + \ 16 \times 11 \over 11\times17} = } \) \({\color{red}{295 \over 187}}\)

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. \({7 \over 11} \ + \ {16 \over 17} = \)\( \ {7 \times 17 \ + \ 16 \times 11 \over 11\times17} =\)\({295 \over 187}\)

10)\({8 \over 9} \ + \ {15 \over 10} = \)\( \ \color{red}{{8 \times 10 \ + \ 15 \times 9 \over 9\times10} = } \) \({\color{red}{215 \over 90}}\)\(\color{red}{ = {215 \div 5 \over 90 \div 5} = {43 \over 18}} \)

GCF(215,90) = 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. \({8 \over 9} \ + \ {15 \over 10} = \)\( \ {8 \times 10 \ + \ 15 \times 9 \over 9\times10} = \)\({215 \over 90}\)

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

How to Add and Subtract Fractions