Mixed numbers and improper fractions

Diagram showing 4 full circles (1, 2/2, 3/3, 4/4) explaining fractions

A whole number can be written as \frac{2}{2}, \frac{3}{3}, \frac{4}{4}, etc.

So 1 \frac{2}{3} can be written as:

\frac{3}{3} + \frac{2}{3} = \frac{5}{3}

Mixed numbers

1\frac{2}{3} is known as a mixed number, because it is made up of a whole number and a fraction.

Improper fractions

\frac{5}{3} is called an improper fraction, because the top number is bigger than the bottom number.

Converting from a mixed number to an improper fraction

You can write the whole number part as a fraction, with the same denominator as the other fraction, and then add the fractions together.

Example

1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}

Here is another example:

2 \frac{1}{4} = 1 + 1 + \frac{1}{4} = \frac{4}{4} + \frac{4}{4} + \frac{1}{4} = \frac{9}{4}

Converting from improper fractions to mixed numbers

You can separate the fraction into as many whole numbers as possible, with a smaller remaining fraction.

Example

\frac{17}{5}= \frac{5}{5} + \frac{5}{5} + \frac{5}{5} + \frac{2}{5} = 3 \frac{2}{5}

Another way to convert an improper fraction is to find how many whole numbers you get, by using a division.

For example let's convert \frac{17}{5} to a mixed number again.

We start by dividing the top number by the bottom number.

{17} divided by {5} is {3} remainder {2}.

So the whole number part is {3}, and the remainder {2} means there are \frac{2}{5} left over.

So the answer is \frac{17}{5} = 3 \frac{2}{5}

Question

Write \frac{20}{7} as a mixed number.

Method 1:

\frac{20}{7} = \frac{7}{7} + \frac{7}{7} + \frac{6}{7} = {2}\frac{6}{7}

Method 2:

\frac{20}{7} = 20 \div 7 = 2 remainder {6}, so:

\frac{20}{7} = 2 \frac{6}{7}

Using a calculator

Example of a fraction button on a calculator

If your calculator has a fraction button you can use this to convert from improper fractions to mixed numbers. Type in the improper fraction, press ' {=}', and the calculator will convert it to a mixed number.