When adding and subtracting fractions *the denominators of both fractions must be the same*. In other words, they must have a **Common Denominator**.

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 with it. Repeat the process using the other denominator. Both denominators should now be the same.

Next, add the numerators. *Keep the common denominator for the answer* - in other words, do NOT add the denominators. Finally, if possible, simplify.

The process for subtraction is the same, but subtract the numerators.

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

The denominators, 5 and 7, will be used to multiply the other fraction:

`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)`

Answer: `frac(22)(35)`

Calculate `frac(1)(6)` - `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)`

Answer: `frac(1)(12)`

See also Lowest Common Multiple

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