Mixed numbers and improper 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.