Maths Quiz - Percentages 3 (Difficult) (Answers)
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!
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(12 ÷ 240) x 100 = (12 × 100) ÷ 240 = 1,200 ÷ 240 = 5%
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(60 ÷ 400) × 100 = (60 × 100) ÷ 400 = 15%
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 |
We are trying to find what percentage of 800 72 is:
(72 ÷ 800) × 100 = (72 × 100) ÷ 800 = 7,200 ÷ 800 = 9% |
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This question asks you to reverse the usual process:
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 |
(30 ÷ 8) x 100% = (30 × 100) ÷ 8 = 3,000 ÷ 8 = 375%
In ‘top-heavy’ fractions (e.g. 30?8), the percentage will be more than 100% |
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(48 ÷ 72) x 100 = (48 × 100) ÷ 72 = 4,800 ÷ 72 = 66.66%
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% |
(96 ÷ 320) x 100 = (96 × 100) ÷ 320 = 9,600 ÷ 320 = 30%
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 |
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(1,840 ÷ 8,000) x 100 = (1,840 × 100) ÷ 8,000 = 184,000 ÷ 8,000 = 23%
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 |
(81 ÷ 900) x 100 = (81 × 100) ÷ 900 = 8,100 ÷ 900 = 9%
Of course, 900 is 100 x 9, so you could work the answer out by simply dividing 81 by 9: 81 ÷ 9 = 9 |
(660 ÷ 1,500) x 100 = (660 x 100) ÷ 1,500 = 66,000 ÷ 1,500 = 44%