# Multiplication: Mixed Numbers

A mixed number is a number expressed as the sum of a whole number and a fraction , such as $3\frac{1}{4}$ .

We should write mixed numbers as improper fractions before multiplying. If the fractions have common factors in the numerators and denominators, we can simplify before we multiply.

Example 1:

Find the product. Write in simplest form.

$1\frac{2}{5}\cdot 2\frac{1}{2}$

First, write the mixed numbers as improper fractions.

$\begin{array}{l}1\frac{2}{5}=\frac{7}{5}\\ 2\frac{1}{2}=\frac{5}{2}\end{array}$

So, the expression becomes

$\frac{7}{5}\cdot \frac{5}{2}$

Simplify.

$=\frac{7}{\underset{{1}}{\overline{)5}}}\cdot \frac{\stackrel{{1}}{\overline{)5}}}{2}$

$=\frac{7}{1}\cdot \frac{1}{2}$

$=\frac{7}{2}$

Write the improper fraction as a mixed number.

$=3\frac{1}{2}$

So,

$1\frac{2}{5}\cdot 2\frac{1}{2}=3\frac{1}{2}$ .

Example 2:

Find the product.

$1\frac{1}{4}\cdot 3\frac{5}{9}$

First, write the mixed numbers as improper fractions.

$\begin{array}{l}1\frac{1}{4}=\frac{5}{4}\\ 3\frac{5}{9}=\frac{32}{9}\end{array}$

So, the expression becomes

$\frac{5}{4}\cdot \frac{32}{9}$

The GCF of $4$ and $32$ is $4$ .

So, to simplify the fractions, divide $4$ and $32$ by $4$ .

$\begin{array}{l}=\frac{5}{\underset{{1}}{\overline{)4}}}\cdot \frac{\stackrel{{8}}{\overline{)32}}}{9}\\ =\frac{5}{1}\cdot \frac{8}{9}\end{array}$

Multiply the numerators the denominators separately.

$=\frac{40}{9}$

Write the improper fraction as a mixed number.

$=4\frac{4}{9}$

So,

$1\frac{1}{4}\cdot 3\frac{5}{9}=4\frac{4}{9}$ .