# Mathematics Methods

It is often useful to express numbers as a percentage when you need to make a comparison of different results. Imagine two people take a test and their scores need to be compared. Which of the following is a better result?

67 out of 98
or
71 out of 96

OK, so the answer to this may already be obvious to you at first glance but it isn’t always so obvious. What about the following two scores?

27 out of 42
or
31 out of 49

Now it’s not quite so obvious which is the better result. Well one easy way is to express these numbers as a percentage instead. If you are wondering what a percentage is, it’s just another fraction like the ones above but instead we express the scores as if they were out of 100. If we do that to all of the scores then it’s much easier to make comparisons.

To understand this, take a score of 7 out of 10. It’s fairly easy to imagine that if the test had twenty questions, the result would have been 14 out of 20. For thirty questions in the test it would have been 21 out of 30 and so on. If we take this all the way to a hundred the result would be 70 out of 100. Or 70%.

So although in the original test, the result was actually 7 out of 10 questions correct, it’s equivalent to 70%.

In fact the symbol % is just a short hand for out of 100 or divided by 100 so in fact it is just another fraction. The following all mean the same thing.

70 out of 100
70/100
70%

So back to the original question of which is the better result of

27 out of 42
or
31 out of 49

We need to adjust results as if they were both out of 100 to make a comparison. Now the numbers here aren’t as straight forward as the 7 out of 10 example above so the simple way to do this is to calculate the fractions first and then multiply by 100.

27 out of 42 is the same as 27/42
Then we simply convert the fraction into a decimal 27/42 = 0.64 and then multiply that by 100.

27/42 x 100= 64%

The second result 31 out of 49 would be

31/49 x 100 = 63%

It is now much easier to compare the two results of 64% compared to 63% to see a clear winner. OK maybe not a clear winner but it is clear which is the better score, even if only slightly better.