Example of Addition and Subtraction of Fractions

To add or subtract fractions with the same denominator we must add or subtract the numerators and leave the same denominator. If instead, we want to add or subtract fractions of different denominators we have first that convert them into equivalent fractions that contain the same denominator and then perform the operation.

Example of addition and subtraction of fractions with the same denominator:
1) 3/7 + 4/7 = 7/7
2) 14/4 + 5/4 = 19/4
3) 7/9 – 3/9 = 4/9
4) 10/3 – 5/3 = 5/3
5) 3/8 + 4/8 = 7/8
6) 7/6 - 5/6 = 2/6
If the denominator is the same, we add or subtract the numerators and leave the denominator the same.
Example of addition and subtraction of fractions with different denominators:
1) ¼ + 2/3 = 11/12
The denominator of the result (12) is a multiple of 3 and 4, since 3x4 = 12. Then we proceed as follows: we take the obtained denominator (12) and divide it by the denominator and then we multiply it by the numerator of one of the fractions. To make this example clearer we have that: 12/4 = 3 and then 3x1 = 3

On the other hand: 12/3 = 4 and then 4x2 = 8
To finish we add the figures obtained, that is, 3 + 8 = 11, which is the value of the numerator of the sum of the fractions.

2) 4/4 -8/16 = 32/64

Process:
16x4 = 64 (denominator of subtraction of fractions)
64/4 = 16 and 16x4 = 64
64/16 = 4 and 4x8 = 32
64-32 = 32 (numerator of subtraction of fractions)
In turn, we can simplify the fraction 32/64, that is, obtain another equivalent fraction by dividing both factors by the same number. In this example we can divide by the number 32 and we get: 32/32 = 1 and 64/32 = 2. Equivalent fraction ½.

3) 6/12 – 1/4 = 12/48

Process:
12x4 = 48 (denominator of the subtraction of the fractions)
48/12 = 4 and 4x6 = 24
48/4 = 12 and 12x1 = 12
24-12 = 12 (denominator of subtraction of fractions)
Final result: 12/48, which is a fraction equivalent to ¼ if we divide the numerator and denominator by 12.

4) ½ + 4/5 = 13/10

Process:
2x5 = 10 (denominator of the sum of the fractions)
10/2 = 5 and 5x1 = 5
10/5 = 2 and 2x4 = 8
5 + 8 = 13 (numerator of the sum of the fractions)