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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, $2/3*5/2=(2*5)/(3*2)=10/6=5/3$

Alternatively, we could cancel the 2 at the top of the 1st term, and the 2 at the bottom of the 2nd term, since $2/2=1$ . Thus, we have $1/3*5/1=5/3$

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, $1\dfrac{1}{2}*1/2=3/2*1/2=3/4$

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, $\dfrac{3/4}{1/4}=3/4*4/1=3$

Dividing mixed numbers

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