# Mixed Numbers

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

It is usually easier to do calculations with improper fractions than mixed numbers, but mixed numbers give a better idea of the size of a number. So you should know how to convert back and forth.

**
Example:
**

Write the mixed number $3\frac{1}{4}$ as an improper fraction.

First, write the mixed number as a sum of a whole number and a proper fraction. Then write the two parts with common denominator , and add.

$3+\frac{1}{4}=\frac{12}{4}+\frac{1}{4}=\frac{13}{4}$

Once you're used to this, you can use a
**
shortcut method:
**

1) Multiply the whole part by the denominator of the fractional part, and add the numerator of the fractional part. This is the numerator of the improper fraction.

2) Keep the same denominator.

In the above example: $3\left(4\right)+1=13$ so $13$ is the numerator, and the denominator is $4$ .

**
Example:
**

Write the improper fraction $\frac{27}{5}$ as a mixed number.

First, divide the numerator by the denominator.

$27\xf75=5\text{R}2$

We get a quotient of $5$ , with a remainder of $2$ .

Use the quotient as the whole part of the mixed number.

Use the remainder as the numerator of the fractional part.

Keep the denominator the same.

$\frac{27}{5}=\frac{25}{5}+\frac{2}{5}=5\frac{2}{5}$