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Expressing one amount as a percentage of another: further examples

In the previous step, we saw that to express one amount as a percentage of another amount the first step is to create a fraction. It is important that students are fluent in a number of methods of converting a fraction into a percentage.

Method 1.

Use equivalent fractions to make the denominator to be a hundred. This is a useful method to emphasise that finding a percentage means scaling up to be out of a hundred. This enables different proportions to be compared. It is useful to compare this to supermarket pricing where the cost per 110g or 100ml is given in order to facilitate price comparison. The disadvantage with this method is that often scaling up to a hundred is not simple e.g. if we have 12 milk chocolates out of a total of thirty. In this case, students need to choose an alternate method.

Method 2.

The unitary method technique, discussed in the Proportion, Scaling, and Ratio course, can be employed. In this case.

Scale the denominator down to be out of 1, before scaling up to be out of 100.

This is not the most efficient method but it does explain where the ‘that number divided by that number times by 100’ rule comes from.

Method 3.

This is the same as method 2 but thinking about the process differently. A fraction can be converted to a decimal by dividing the numerator by the denominator: \(12 \div 30\).

We can then change a decimal to a percentage by multiplying by a hundred. Method 3 is more efficient than method 2. Method 2 can be used as a stepping stone to explain why method 3 works.

Methods 2 and 3 require the use of a calculator when the numbers do not easily scale up to 100. It is important that students are fluent in Method 1 for when a calculator is not available and the numbers are easily scalable to 100, for example in a non-calculator examination.

Problem worksheet

Now complete questions 6, 7 and 8 from this week’s worksheet using appropriate methods from above.
As a reminder, the worksheet can be found in the first step of this week.

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This article is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre