Mixed numbers and improper fractions

In a nutshell

A mixed number is a number which consists of a whole number and a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Example 1

Below are some examples of mixed numbers:

$2\frac{1}{2}, 5\frac{1}{4}, 8\frac{3}{10}$ 

Below are some examples of improper fractions:

$\frac{13}{2}, \frac{7}{7}, \frac{27}{5}$ 

Writing a mixed number as an improper fraction

procedure

1.	Multiply the whole number by the denominator of the fraction part.
2.	Add the answer to Step 1 to the numerator of the fraction part.
3.	Write the answer to Step 2 over the denominator of the fraction part.

Example 2

Convert the following mixed number into an improper fraction:

$2\frac{7}{9}$ 

Multiply the denominator and the whole number:

$2 \times 9 = 18$ 

Add the answer to the previous step to the numerator:

$18+7 = 25$ 

Write the answer to the previous step above the denominator.

$\underline{\frac{25}{9}} (= 2\frac{7}{9})$ 

Writing an improper fraction as a mixed number

procedure

1.	Divide the numerator by the denominator using long division with remainders.
2.	Write down the whole number result.
3.	Write the remainder over the denominator of the original improper fraction. This will be the fraction part of the mixed number. Note: If there is no remainder, the answer is a whole number with no fraction part.
4.	Simplify the fraction part if required.

Example 3

Convert the following improper fraction into a mixed number:

$\frac{23}{7}$ 

Divide the numerator by the denominator:

$23 \div 7 = 3\thinspace R\thinspace2$ 

The whole number part is 3. The remainder is written over the original denominator.

$\underline{3\frac{2}{7}}(=\frac{23}{7})$ 

Note: The fraction part in this example cannot be simplified.