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Comparisons: percentages

To talk about a percentage on its own can make little sense and can be misleading.
7.4
MICHAEL ANDERSON: Percentages help us to express proportions out of 100.
11.1
PAULA KELLY: Comparing percentages is simple, so long as we’re comparing percentages of the same amount.
17.1
MICHAEL ANDERSON: So 36% of 12 must be greater than 28% of 12.
22.1
PAULA KELLY: 12% of 20 is less than 15% of 20.
26.5
MICHAEL ANDERSON: And 26% of 90 is bigger than 18% of 90.
30.8
PAULA KELLY: However, if I had to compare 26% of 20 with 18% of 36, we’d have to calculate them both to compare them. We can’t just compare the percentages by themselves.
To talk about a percentage on its own can make little sense and can be misleading. When talking about a percentage it is important that we consider ‘the whole’.
We have to ask ourselves: what are we taking a percentage of? What would 100% be?

Example

According to a 2012 study, about 3% of the population of Ireland speak Irish as their first language, and about 16% of the population of Luxembourg speak French, does this mean that there are more French speakers in Luxembourg than there are Irish speakers in Ireland?
Well, no. We need to know the populations of Ireland and Luxembourg in order to answer this question. In 2012, the population of Ireland was approximately 4.5 million, meaning there were approximately 135,000 people speaking Irish as their first language. By comparison, in 2012, the population of Luxembourg was about half a million, meaning there were about 80,000 French speakers in Luxembourg.
Whilst the proportion was greater in one country, ‘the whole’ population was much lower. Percentages must be considered with respect to ‘the whole’.

Problem worksheet

Now complete question 1 from this week’s worksheet.
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Maths Subject Knowledge: Fractions, Decimals, and Percentages

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