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Percentages 3 (Difficult)
So, you have made it to the third of our Difficult level Eleven Plus maths quizzes on Percentages – give yourselves a pat on the back! As you will know by now, percentages are a way to represent proportions of numbers, but how do you calculate them? In the last quiz we showed you one method. Here’s another which you might prefer:
What percentage of 70 is 28?
First divide 70 by 100 to work out what 1% of 70 is:
70 ÷ 100 = 0.7
Next, divide 28 by 0.7 to work out how many “lots” of 1% are in 28:
28 ÷ 0.7 = 40
So, there is your answer: 28 is 40% of 70
This method is great for estimating your answers, but it often requires a calculator!
So now, on with the quiz. You can use the method above, or the one we showed you in our previous quiz. Alternatively, you may have your own method. Use whichever you prefer – as long as it gives you the right answer!
In ‘top-heavy’ fractions (e.g. 30⁄8), the percentage will be more than 100%
Of course, 900 is 100 x 9, so you could work the answer out by simply dividing 81 by 9:
81 ÷ 9 = 9
(Give your answer to two decimal places)
If you know your times tables, you might have spotted that 72 is 6 x 12 and 48 is 4 x 12. 4 is two-thirds of 6 so the percentage will be equivalent to two-thirds, i.e. 66.66%
(660 ÷ 1,500) x 100 = (660 x 100) ÷ 1,500 = 66,000 ÷ 1,500 = 44%
(72 ÷ 800) × 100 = (72 × 100) ÷ 800 = 7,200 ÷ 800 = 9%
Don’t be put off by large numbers – they can often be rounded down by removing any zeros, e.g. 184,000 ÷ 8,000 is the same as 184 ÷ 8
That is the amount of red cars, but we want to know the percentage that are not red:
100 - 30 = 70, so 70% of the cars are not red
Of course, you may have spotted that 400 is 4 x 100, so you could work this out more quickly by just dividing 60 by 4: 60 ÷ 4 = 15
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To find 20% of 40, divide by 100 then times by 20:
40 ÷ 100 = 0.4
0.4 x 20 = 8
A quicker way to find 20% is to simply divide by 5 (because 20% is the same as one-fifth)
40 ÷ 5 = 8