Mixed numbers and improper fractions

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

The number one can be written as any fraction where the numerator (top number) and denominator (bottom number) are the same:

\[1 = \frac{2}{2} = \frac{3}{3} = \frac{4}{4} ...\]

This means you can write any whole number as a fraction where the numerator is a multiple of the denominator:

\[2 = \frac{4}{2} = \frac{6}{3} = \frac{8}{4} ...\]

\[3 = \frac{6}{2} = \frac{9}{3} = \frac{12}{4} ...\]

Mixed numbers

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

The whole number can be written as a fraction and the two parts added together.

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

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

Improper fractions

\(\frac{5}{3}\) is called an improper fraction, because the numerator is bigger than the denominator.