Fractions of Amounts and Understanding Percentages

Taking a fraction of a quantity is a key skill and, happily, has a very simple and memorable method. A fraction of an amount is just like a division sum; if you think about taking a half of something, you are dividing it by two. Taking a third is the same as dividing by three, and so on. You are simply dividing by the bottom figure of the fraction.

For instance: Find 1/4 of 256 is exactly the same as saying 256 ÷ 4. That should be straightforward enough using the 'bus shelter' method or any other technique your child likes to employ. The answer is 64.

Now let's get to the more complex ones. Imagine you're asked to find 3/4 of 256.

Three quarters is the same as saying 'three lots of a quarter'. We showed how to find ONE quarter of 256, so what we need to do is find THREE quarters of that number. In other words, three lots of one quarter. So, as we know one quarter of 256 is 64, three quarters of 256 must be three lots of 64. 3 x 64 = 192 and that is the answer.

What this boils down to is the following memorable chant which children seem to grasp quickly.

'DIVIDE BY THE BOTTOM, TIMES BY THE TOP'

Finding a fraction of an amount is exactly the same as multiplying by that fraction.

If you had to find 3/5 of 400 you would take 400, divide it by the bottom number (5) and multiply it by the top number (3). You can do this in either order but it is easier to do the division by the bottom first in most cases.

400 ÷ 5 = 80     80 x 3 = 240     3/5 of 400 = 240

or, the other way round...

400 x 3 = 1200     1200 ÷ 5 = 240

As you can see, it's normally easier to deal with the division first as you use smaller numbers but there will be occasions when the numbers are easier to deal with if you multiply by the top digit first.

I frequently find percentage questions stumping children if they have not been taught the concept well. The idea is straightforward enough - 'per cent' literally means 'out of hundred' so it is really the same as a fraction with '100' on the bottom.

Therefore 31 % is the same as 31⁄100.

There are things that can be done which throw adults, let alone children, when percentages are used. For instance, if a price increases by 10% then drops by 10% of the new price, it won't end up

back at the original price...

Percentages are useful in many ways; they can express change in a way that uses whole numbers rather than decimals or fractions and they can also show an easy-to-understand comparison between two numbers.

What percentage of 20 is 4?

20 is the whole. 4 out of 20 is the quantity we need to establish as a percentage.

We work out a percentage by taking the fraction and multiplying it by 100, so in our example it would become

4⁄20 x 100 = 400⁄20 = 20%

Always remember that a fraction is the same as a division sum. The top number should be divided by the bottom number. This all becomes critical when we convert between fractions, decimals and percentages.