Adding and Subtracting Fractions
# Adding and Subtracting Fractions

GCSE(F),

When adding and subtracting fractions *the denominators of both fractions must be the same*.

Find equivalent fractions for both fractions to be added so that the denominators are the same. The easiest method is to *cross-multiply*. Take the denominator of one fraction and multiply both the numerator and denominator of the other fraction. Repeat the process for the fraction the other way around. Both denominators should now be the same.

Next, add the numerators, *keeping the same denominator for the answer*. Finally, if possible, simplify.

The process for subtraction is the same: and only the numerators are subtracted.

## Examples

1. What is `frac(1)(5)` + `frac(3)(7)`?

Answer: `frac(22)(35)`

The denominators, 5 and 7, have a lowest common multiple (both go into) 35:

`frac(1)(5)+frac(3)(7)`

`=frac(1^(times7))(5_(times7))+frac(3^(times5))(7_(times5))`

`=frac(7)(35) + frac(15)(35)`

`=frac(22)(35)`

2. Calculate `frac(1)(6)` - `frac(1)(12)`.

Answer: `frac(1)(12)`

The denominators, 6 and 12, have a lowest common multiple of 12:

`frac(1)(6)-frac(1)(12)`

`=frac(1^(times2))(6_(times2))-frac(1)(12)`

`=frac(2)(12)-frac(1)(12)`

`=frac(1)(12)`

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