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# Working with ratio

Even though ratio may not be explicitly taught as a distinct mathematical concept until the middle years of schooling, it is encountered in the earlier work done with equivalent fractions.

Equivalent fractions express the same ratio.

For example, \(\frac 4 6\) is equivalent to \(\frac 6 9\) because both express the underlying ratio of \(\frac 2 3\).

Understanding how to maintain the constant multiplicative relationship between two amounts is the foundation of proportional reasoning.

To create another equivalent fraction, we need to use multiplication on the numerator and denominator and keep the ratio constant. In this example, we multiply both the numerator and the denominator by 3.

That is, \(\frac 4 6\) = \(\frac {12}{18}\).

Modelling ratio using objects allows manipulation of the groups to reveal the underlying ratio. Watch the video *Comparing Ratios*.

You can download the *Comparing Ratios* video transcript.

For more information, read the article *Modelling Proportional Thinking with Twos and Threes* on the AAMT website.