Teaching mathematics

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# 3 Connecting ratio and proportional reasoning

According to the Oxford English Dictionary (OED) Online, ratio is defined as ‘the quantitative relation between two amounts showing the number of times one value contains or is contained within the other’.

For example, the ratio of male to female professors is 4 to 1.

In contrast, proportion is described by the OED as a part, share, or number considered in comparative relation to a whole.

For example, the proportion of greenhouse gases in the atmosphere is rising.

In other words, a ratio is used to describe a comparison between two (or more) objects, amounts or values, and a proportion is used to describe one object, amount or value, using a comparison to a whole.

For example if the ratio of boys to girls in the class is 2 to 3, or 2:3, the proportion of boys is 2/5.

Since the proportion of boys in the class is expressed as a fraction of a whole, it is not necessary to know the proportion of girls. If there are 30 children in the class and 2/5 of them are boys, it can be inferred that 3/5, or 18, of them are girls.

In contrast, when expressed as a ratio, the ‘2’ is meaningless without the comparison to the ‘3’.

Proportional thinking and reasoning is knowing the multiplicative relationship between the base ratio and the proportional situation to which it is applied.

Understanding ratio and proportion is more than merely being able to perform appropriate calculations, being able to apply rules and formulae or manipulating numbers and symbols in proportion equations.

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