Converting between the three forms, the four operations with fractions, percentage change and reverse percentages, rounding, estimation and bounds.
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1.How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example 3 divided by 8 = 0.375.
2.How do you convert a decimal to a percentage?
Multiply by 100. For example 0.375 becomes 37.5 per cent.
3.How do you convert a percentage to a fraction?
Write it over 100 and simplify. For example 40 per cent = 40 over 100 = 2 over 5.
4.How do you add or subtract fractions?
Rewrite both with a common denominator, then add or subtract the numerators only.
5.Work out 2 over 3 plus 1 over 4.
Common denominator 12: 8 over 12 plus 3 over 12 = 11 over 12.
6.How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify.
7.How do you divide fractions?
Turn the second fraction upside down and multiply.
8.Work out 3 over 4 divided by 2 over 5.
3 over 4 multiplied by 5 over 2 = 15 over 8.
9.How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
10.How do you find a percentage of an amount?
Convert the percentage to a decimal and multiply. For 15 per cent of 80, work out 0.15 x 80 = 12.
11.What multiplier increases an amount by 20 per cent?
1.2
12.What multiplier decreases an amount by 15 per cent?
0.85
13.State the equation for percentage change.
percentage change = (change divided by original amount) x 100
14.A price rises from 40 to 50. Calculate the percentage increase.
Change is 10. 10 divided by 40 = 0.25, so 25 per cent.
15.What is a reverse percentage question?
One where you are given the amount after a change and asked for the original.
16.After a 20 per cent increase an item costs 60. Find the original price.
Divide by the multiplier: 60 divided by 1.2 = 50.
17.Why do you divide rather than subtract in reverse percentage questions?
The percentage was applied to the original amount, not the new one, so subtracting the same percentage gives the wrong answer.
18.How do you round to 2 significant figures?
Count from the first non-zero digit, keep two digits, and round the second using the digit after it.
19.Round 0.004736 to 2 significant figures.
0.0047
20.Round 3849 to 2 significant figures.
3800
21.How do you estimate a calculation?
Round every number to 1 significant figure, then work it out.
22.Estimate 19.6 x 4.2.
Round to 20 x 4 = 80.
23.What is the upper bound of a length given as 12 cm to the nearest cm?
12.5 cm.
24.What is the lower bound of that same length?
11.5 cm.
25.How do you find the highest common factor of two numbers?
Write each as a product of prime factors and multiply the factors they share.
26.How do you find the lowest common multiple?
Write each as a product of prime factors and multiply the highest power of every prime that appears.
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