Increasing, decreasing, and working backwards to the original.
6 lessons · 35 questions (A–G) · 20 calculation + 15 word problems · no time pressure
Percentage problems grow or shrink an amount by a given percentage — sales, pay rises, VAT, interest — and the quickest method is a multiplier, so a 12% rise means × 1.12. The trickiest type is the reverse percentage, where you know the final amount and work back to the original. Pupils most often slip by adding the percentage on instead of using the multiplier, or by treating a reverse percentage like a normal one.
At Improve Tuition, a qualified teacher builds the multiplier method until it is automatic, then tackles reverse percentages carefully, in small worked steps — with read-aloud, comfort spacing and a reading tint for pupils who take in maths more easily that way.
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Lesson 1
A percentage of an amount
Aim: Find a percentage of an amount using easy building blocks.
Per cent means “out of 100”. The easy pieces are 10% (divide by 10), 1% (divide by 100) and 50% (halve).
Build the percentage you need from these. For example, 35% = 10% + 10% + 10% + 5%.
Combine percentage steps and reason through multi-step problems.
Success criteria — I can:
apply each change in turn
use multipliers where you can
check the answer is sensible
31.A £200 coat is increased by 10%, then that new price is reduced by 10%. What is the final price?
Answer:
Show working
£200 × 1.1 = £220.
£220 × 0.9 = £198 (not back to £200).
32.VAT at 20% is added to a £150 bill, then a 10% discount is taken off the total. What is the final amount?
Answer:
Show working
£150 × 1.2 = £180.
£180 × 0.9 = £162.
33.A town of 5000 people grows by 6% in year one and 5% in year two. What is the population after two years?
Answer:
Show working
5000 × 1.06 = 5300.
5300 × 1.05 = 5565.
34.After a 20% discount a bike costs £240. How much money was taken off in the sale?
Answer:
Show working
20% off means £240 is 80% of the original.
Divide by 0.8: £240 ÷ 0.8 = £300.
Taken off = £300 − £240 = £60.
35.£2000 is invested at 5% simple interest per year. What is the total value after 3 years?
Answer:
Show working
Interest each year = 5% of £2000 = £100.
Over 3 years: 3 × £100 = £300.
Add to the start: £2000 + £300 = £2300.
0 of 35 answered
Guide
How do you increase or decrease by a percentage?
To change an amount by a percentage, the quickest way is a multiplier. To increase by 15%, multiply by 1.15; to decrease by 15%, multiply by 0.85. The multiplier does the whole job in one step.
A reverse percentage works the other way: you are given the amount after a change and asked for the original. Since the final amount equals the original times the multiplier, you divide by the multiplier to get back to the start.
Common mistakes. Forgetting to add or subtract the percentage you worked out, using the wrong multiplier (1.15 instead of 0.85 for a fall), or solving a reverse percentage as if it were an ordinary increase.
Common questionsWhat is a multiplier in percentages?
A multiplier is a single number that applies a percentage change in one step. A 20% increase uses × 1.2; a 20% decrease uses × 0.8.
How do you increase an amount by a percentage?
Multiply by 1 plus the percentage as a decimal. To increase £50 by 10%, work out 50 × 1.1 = £55.
How do you decrease an amount by a percentage?
Multiply by 1 minus the percentage as a decimal. To decrease £50 by 10%, work out 50 × 0.9 = £45.
What is a reverse percentage?
It is finding the original amount when you only know the amount after a percentage change. You divide the final amount by the multiplier that was used.
How do you find a percentage change?
Work out the difference, divide by the original amount, then multiply by 100. A rise from 40 to 50 is 10 ÷ 40 × 100 = 25%.
Stuck on this topic?
A teacher can find the exact gap
Practising percentages on your own is a strong start. If the same marks keep slipping, a qualified teacher can pinpoint the precise gap and fix it. Improve Tuition offers one-to-one maths tuition with our maths tutors in Batley and online — the first assessment is free.