# Fractions

A
**
fraction
**
is a way of expressing division.

$\frac{a}{b}$ means $a\xf7b$ .

This notation can be used to represent numbers which are not
whole numbers
**
.
**

The number below the bar is called the
**
denominator
**
. It tells the number of equal parts into which the whole has been divided.

The number above the bar is called the
**
numerator.
**
It tells how many of the equal parts are being considered.

**
Example 1:
**

$\frac{2}{5}$ means $2\xf75$

The whole has been divided into $5$ parts and $2$ are being considered.

The fraction $\frac{2}{5}$ can be represented by a shape divided into $5$ pieces of equal size, with $2$ of them shaded.

A
**
proper fraction
**
is a fraction whose numerator is less than its denominator. If the numerator is greater than the denominator, then it is an
improper fraction
**
.
**

**
Example 2:
**

$\frac{3}{7}$
is a
**
proper fraction
**
. It can be represented by a shape divided into
$7$
pieces of equal size, with
$3$
of them shaded.

$\frac{14}{5}$
is an
**
improper fracti
**
**
on
**
. It is greater than
$1$
, so to draw it, you'll need more than
$1$
shape. In fact it needs
$3$
equal shapes, each divided into
$5$
pieces of equal size, and
$14$
of them shaded.

A number which consists of a
whole number
plus a fraction is a
mixed number
**
.
**
Mixed numbers can be written as an improper fraction and an improper fraction can be written as a mixed number.
The improper fraction above can be written as
$2\frac{4}{5}$
.

**
Example 3:
**

Write $7\frac{2}{5}$ as an improper fraction.

$7\frac{2}{5}=\frac{7}{1}+\frac{2}{5}$

$=\frac{7\text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}5}{1\text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}5}+\frac{2}{5}$

$=\frac{35}{5}+\frac{2}{5}$

$=\frac{37}{5}$

**
Example 4:
**

Write $\frac{11}{7}$ as a mixed number in simple form.

$\frac{11}{7}=11\xf77=1\text{R}4$

Therefore, $\frac{11}{7}=1\frac{4}{7}$ .

A fraction is in lowest terms when the numerator and denominator have no common factor other than $1$ . To write a fraction in lowest terms, divide the numerator and denominator by the greatest common factor .

**
Example 5:
**

Write $\frac{45}{75}$ in lowest terms.

$45$ and $75$ have a common factor of $15$ .

$\frac{45}{75}=\frac{45\text{\hspace{0.17em}}\xf7\text{\hspace{0.17em}}15}{75\text{\hspace{0.17em}}\xf7\text{\hspace{0.17em}}15}=\frac{3}{5}$

See also fraction operations .