Changing fractions into percentages I know that to change a fraction into a percentage you do numerator divided by denominator then times by 100. Why do you do numerator divided by denominator?

Answer 1

Because dividing part of something by the whole lot gives an index between 0 and 1. Multiplying it by 100 is just a convention to make it easier to read.

For example:

8 out of 10 cat owners say their cats prefer kit-e-kat.

10 is the whole lot of owners surveyed, and 8 is the number of owners we're talking about. That's written as

8

--

10

8/10 is 0.8, which is the index number between 0 and 1, and multiplying by 100 makes it 80% which is easy to read.

The reason you'd want to make this index (percentage) is to compare different figures easily.

For example

3 out of 5 dog owners say their dogs prefer pedigree chum.

2/5 = 0.6 = 60%

8/10 and 3/5 are a bit difficult to compare, but by making the index (percentage) it's easy to see how much more popular kit-e-kat is among cat owners' cats than pedigree chum is among dog owners' dogs.

So there you go: the reason for dividing the top number by the bottom number is to get an index by which comparing is easy. And the multiplying by a hundred part is just to make it look pretty. (^_^)