Adding and Subtracting the fractions

A fraction has two parts in them. One is the upper number called the numerator. The other is the lower number called the denominator.

For example, in the fraction , 5 is the numerator and 8 is the denominator of the fraction.

Like fractions are those which have the same lower numbers. Unlike fractions are those which have different lower numbers.

For example,  and   are like fractions.  and    are unlike fractions.

The Calculator:

With the help of this calculator, one can easily add or subtract the fractions. Firstly, we have to input the number of fractions. After that input the numerator and the denominator. Meanwhile, input the operator between the fractions. Then click on the ''Calculate'' button. This will calculate the result and will also show the work. If we have to input other fractions then click on the ''Clear'' button.

Facts, Theorems, and Laws:

·          '+' * '-' = '-'. For example, 5 + (-3) = 5 – 3 = 2

·         '-' * '-' = '+'. For example, 4 - (-4) = 4 + 4 = 8

·         The sign before an unsigned number is '+'.

·         The operation is subtraction if '+' and '-' sign is present before the numbers. But the sign of the result depends upon the numbers. For example, +6 – 8 = -2 and +9 - 5 = +4

·         The operation is an addition if '+' and '+' sign is present and '+' is the sign of the result.

When '-' and '-' sign is present then the operation is '+' and '-' is the sign of the result.

Calculations of like fractions:

Calculations of like fractions are very simple. We have to add or subtract the numerator. After adding or subtracting the result gets shared with a common lower number, which gives the final result.

For example, we have to do following calculations

Calculation Steps:

Calculate the numerator

1 + 2 + 1 - 3 + 6 + 1 + 4 - 9 + 7 – 7 = 3

Therefore, the result is 15/8.

Addition or subtraction of unlike fractions:

To add or subtract unlike fractions, firstly, we have to find the Least Common Denominator (LCD).

For example, calculate the following fractions

The LCD of given fractions is 24. Now we have to multiply the lower numbers of each fraction with such numbers to get the LCD. And multiply the upper number by that number with which you have multiplied the lower number.

Therefore,

Now in all the fractions, we have 24 as the LCD. Also, it becomes a like fraction having 24 as the lower number. So, we have to add or subtract the numerator. Then sharing the result with common lower numbers, we get the result.

10 + 8 – 8 + 10 + 10 + 12 - 36 + 3 + 0 + 8 = 17

Therefore, the result is .