Using Percentages to Compare
# Using Percentages to Compare

GCSE(F),

Because percentages are always *out of a hundred*, they can be easily used to compare different results.

Change results from two different quantities to a percentage figure, and then compare the percentages.

To obtain the percentage figure, divide the result by the total, then multiply by 100.

## Examples

1. Which is greater, 35 out of 90, or 42 out of 110?

Answer: 35 out of 90

35 out of 90 = `frac(35)(90)` x 100 = 38.9% (1dp)

42 out of 100 = `frac(42)(110)` x 100 = 38.2% (1dp)

The first calculation gives the higher percentage and is therefore greater.

2. A shirt is on sale at £12 instead of the normal price of £18. A jacket is on sale for £39 instead of the normal price of £55. Which, as a percentage, offers the larger saving?

Answer: The shirt

The new price of the shirt:

12 out of 18 = `frac(12)(18)` x 100 = 66.7% (1dp)

The new price of the jacket:

39 out of 55 = `frac(39)(55)` x 100 = 70.9% (1dp)

In percentage terms, the shirt is the larger saving.

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