# 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).