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**Multiplying fractions**

When multiplying fractions, you can cross-cancel common factors, and then multiply numerator by numerator, and denominator by denominator. You don’t necessarily need to cross-cancel common factors but it simplifies the problem for you.

For example,

Alternatively, we could cancel the 2 at the top of the 1st term, and the 2 at the bottom of the 2nd term, since . Thus, we have

We reach the same answer, but cancelling is easier if you have very large numbers, or you will take forever to simplify.

**Multiplying mixed numbers**

When multiplying mixed numbers, it is necessary to convert them first to improper fractions, and then multiply.

For example,

**Dividing fractions**

To divide by a fraction, you multiply by its reciprocal (i.e. inverted, such that for the dividing fraction, put the top on the bottom, and the bottom on the top).

For example,

**Dividing mixed numbers**

When dividing mixed numbers, first convert to improper fractions, and then divide (i.e. multiply by the reciprocal).

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