Numeracy Skills

Seeing numbers in percentage form considerably simplifies the process of digesting information, comparing and contrasting data, recognising patterns and correlations and subsequently making predictions.

If, for example, you scored 47 out of 100 in one exam and 58 out of 120 in another, it would be difficult to judge in which exam you performed better, until you converted the result into a percentage. A simple way of calculating this figure is to divide the smaller figure by the larger one (which represents 100%) and then multiply by 100:

Exam 1: (47 ÷ 100) x 100 = 47 (%)

Exam 2: (58 ÷ 120) x 100 = 46.6 (%)

and you have your answer.

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In the case of the talking cat question, if we were trying to figure out the initial percentage rate of talking cats then the equation we would be dealing with would be:

(100 ÷ 15000) x 100 = 0.66 (%)

From here, it is easy to work out that the percentage rate of non-talking cats would be 99.33% (100 – 0.66).

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If we were trying to figure out the current percentage rate of talking cats, then the equation would be:

(32,000 ÷ 32,500) x 100 = 98.46 (%)

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Finally, to work out the overall percentage rate of increase in the talking cat population, we need to start with our initial figure, 100, and calculate the % increase from 100 to 32,000.

To do this we first need to work out the initial difference between 100 and 32,000 (i.e. 32,000 – 100) which is 31,900 - this being the raw increase in number of the talking cat population. Then we divide this difference by the original (31,900 ÷ 100) which is 319. Finally, as with our previous equation, we multiply this number by 100 which yields an overall increase rate of 31,900%!

The equation looks like this:

(32,000 – 100) ÷ 100 x 100 = 31, 900 (%)

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It is also sometimes helpful to state values such as these in ratio form (where a relationship between two separate quantities, for example water and cordial, is expressed in number: 4:1 – four parts to one).

Let us say, for the purpose of simplicity, that for every 100 cats, 70 (%) can talk whilst 30 (%) cannot. Here, the ratio of talking to non-talking cats would be 7:3 (ratios are expressed as two numbers separated by a colon: ‘x:y’). The ratio of talking cats to the overall cat population would be 7:10 (for every 10 cats, 7 of them will be talkers – expressed as a fraction, 7/10ths of cats).

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Quick Activity

Bearing the above points in mind, see if you can answer the questions in the Percentages & Ratios Quiz.