## Content description

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

### Equivalent fractions

Equivalent fractions are located on the same place on the number line. The number line shows that \(\dfrac{3}{6}\) and \(\dfrac{1}{2}\) mark the same place. That is, \(\dfrac{3}{6}\) and \(\dfrac{1}{2}\) are equivalent fractions.

### Some important aspects of equivalence

- Equivalent fractions mark the same point on the number line.
- Equivalent fractions can be modelled using areas of rectangles.
- Equivalent fractions to a given fraction can be found by multiplying or dividing the numerator and the denominator of the fraction by the same whole number.
- In simple cases, fractions are 'related' if the denominator of one is a multiple of another. For example, the fractions \(\dfrac{1}{3} \text{and} \dfrac{5}{9}\) have related denominators because 9 is a multiple of 3.
- It is possible for two fractions to be equivalent even when the denominators are not obviously related and the equivalence is not immediately obvious. For example, \(\dfrac{17}{34} \text{and} \dfrac{5}{10}\) are both equivalent fractions since they are both equal to \(\dfrac{1}{2}\).