# Fraction arithmetic

Fractions with the same can be added (or subtracted) by adding (or subtracting) the numerators.

For instance, or .

If two fractions do not have the same denominator, then find a common denominator by making .

### Example

Work out .

Work out the common denominator by looking for the lowest common multiple of 7 and 3. This is 21 ( ).

Write the equivalent fractions using 21 as the new common denominator.

So:

This is the final answer as the fraction cannot be .

Question

Work out .

This sum contains a ( ), which must be converted to an .

• Change the whole number part to a fraction using the denominator of the fraction part. So
• Add on the fraction part:

So

This gives:

Now look for a by looking for the lowest common multiple of 5 and 4 which is 20.

Write equivalent fractions using 20 as the common denominator.

So:

The question was asked in mixed number format, so the answer should be given as a mixed number. is an improper fraction so it can be written as a mixed number.

Divide the by the denominator:

This fraction cannot be simplified further, so this is the final answer.