Using fractions

Fractions show parts of whole numbers, for example, the fraction \(\frac{1}{4}\) shows a number that is 1 part out of 4, or a quarter.

Rectangle split into 4 evenly sized rectangles. 1 shaded, showing a quarter

\(\frac{1}{4}\) is the same as \(1 \div 4\).

Fractions are one way of showing numbers that are parts of a whole. Other ways are decimals and percentages. You can also convert between fractions, decimals and percentages. Like whole numbers and decimals, fractions can be either positive or negative. For example, \(3 \frac{1}{5}\) or \(- \frac{1}{4}\).

Equivalent fractions

Equivalent fractions are fractions that are worth exactly the same even though they are written differently. \(\frac{1}{4}\) is worth the same as \(\frac{2}{8}\) because \(\frac{2}{8}\) will simplify to \(\frac{1}{4}\) by dividing by a common factor of 2.

Fraction wall, showing 1/4 = 2/8

Working out equivalent fractions

Equivalent fractions are made by multiplying or dividing the denominator and numerator of the fraction by the same number.

For example, to find fractions that are equivalent to \(\frac{1}{3}\), multiply the numerator and denominator by the same number.

1/3 x 2 = 2/6

Multiplying or dividing both parts of a fraction by the same number will always create equivalent fractions. There are an infinite amount of equivalent fractions that can be found because there is an infinite amount of numbers to multiply by.


\(\frac{3}{8}\:\) is equivalent to \(\frac{?}{24}\). Find the missing number.

Look at the two fractions to see what multiplier has been used. In this case, the denominators are both known: 8 and 24. 8 has been multiplied by 3 to get a new denominator of 24. This means the numerator also has to be multiplied by 3:

\[3 \times 3 = 9\]

The answer is \(\frac{9}{24}\).