Percentages of Amounts and Converting Fractions to Decimals & Percentages

Percentages of Amounts

It's a common task to have to find the given percentage of an amount. You can use this to increase - or reduce - an amount by a given percentage as well.

a) I want to pick 30% of the strawberries; if there are 50 strawberries, how many will I pick?

There are 50 strawberries and I want 30%, or 30⁄100 of them. That's the same as 3⁄10

Now we find three tenths of 50:

3⁄100 x 50 = 150⁄10 = 15 strawberries

b) The price of a shirt is £9.50. The sale price is 20% less. What is the new price of the shirt?

Firstly, it's worth looking at the sum and deciding which approach is the better. Work out 20% of £9.50 and take it off, or work out what percentage of the original selling price is left and work that out as a price.

For example, we can say that if the price has been reduced by 20%, the new price must be (100% - 20%) 80% of £9.50.

As long as we can work out the percentage left immediately in our heads, this will be the easier way to solve the sum.

So, for our sum, we need to find 80% of the £9.50 selling price.

80% is the same as 80⁄100 so we need to multiply this by £9.50. It'd help if we could cancel the fraction.

Down a bit to give us easier numbers to work with; as 20 fits into both top and bottom, we can change 80⁄100 to 4⁄5

4⁄5 x £9.50 = £38⁄5 = £7.60

Had we taken 20% of the original price and taken it from £9.50, we would get the same answer. If possible, show your child how to do it both ways!

Converting Fractions to Decimals & Percentages

SATs papers require the children to move between the three but entrance tests usually expect it to be done as part of more complex sums. We will look at the basics.

Whenever you see a decimal, it can be easily converted into a percentage and vice-versa. Remember the first space after a decimal point is for TENTHS and the next is for HUNDREDTHS. This means that a two-digit decimal can be interchanged with a percentage.

0.25 = 25% 0.54 = 54%   0.7 = 0.70 = 70%   18% = 0.18

This still works if there are more digits in the decimal number:

0.448 = 44.8%     0.0229 = 2.29%

To convert a decimal to a fraction, it's also worth remembering the tenths and hundredths are the figures after a decimal point.

Therefore 0.6 is the same as six tenths. 0.91 is ninety-one hundredths, and so on. Of course, these figures can usually be simplified and children are expected to be able to present the figures in their lowest form.

Percentages, as they're virtually the same as decimals, can also be changed to fractions easily.
75% = 0.75 = 75⁄100. You then cancel it down to 3⁄4 .

The only real difficulty is converting from a fraction to decimals or percentages. To do this, remember the fraction is the top number divided by the bottom number. The decimal is simply the result of dividing the top number by the bottom number - not easy without a calculator - so children tend to learn key ones like a quarter = 0.25 without mathematical proof.

Percentages are slightly more involved:

9⁄20 as a percentage means you must multiply by 100. It's worth cancelling down the sum.

9⁄20 x 100 is the same as saying 9 ÷ 20 x 100 or, for ease, 9 x 100 ÷ 20 .

You can simplify it by thinking about the net effect of dividing anything by 20 and multiplying by 100. It gives the equivalent of timesing the original number by five. This is because 20 fits into 100 five times. You can always 'cancel down' sums in this way to make them easier.

So, 9⁄20 x 100 = 9⁄1 x 5 (now we've seen how many times 20 fits in to the numbers) = 45%

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