Thjis is fairly simple to do once you have got the hang of percentages. Effectively we need to divide one number by the other and then make that fraction into a percentage by multiplying by 100. This is probably best shown in an example.

### Example 1

Q. “Hannah scored 33 out of 40 marks in her History exam. James did a slightly different assessment, and scored 60 out of 70 marks. Hannah remarks that James did better on his exam. James agrees, pointing out he did nearly twice as well as Hannah!”

Are their statements accurate? What's the first thing we need to do before we can decide? We must begin with working out how to express one quantity as a percentage of another!

A. Well they both did different assessments, so we need something to compare them fairly before we can say for sure. This is really, really easy to do. All we need to do is the following:

1) Just divide each of their scores, by the total for the paper.

Hannah: 33/40 = 0.825 & Junaid: 60/70 = 0.857

Straight away, you can see James did perform better overall, but certainly not by as much double Hannah’s performance.

But, because decimals like this are awkward to work with, we came up with an idea of expressing the decimal as a percentage (you can also do this with fractions)–

2) Multiply numbers like that by 100, and we’ll get a good measure that will reduce the amount of decimals we have to work with. We then call that number a ‘percentage’.

Hannah: 0.825 x 100 = 82.5% & Junaid: 0.857 x 100 = 85.7% - 86%

For an assessment, that would be their percentage scores.

So to express one number as a percentage of another

1. Divide the first number by the second, and then
2. Multiply the result by 100.

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