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KS3 Maths · Number and proportion · Year 7

Percentages of amounts

Find any percentage of any amount — with or without a calculator.

About 20 minutes

Step 1 · Wonder why it matters

Hook

Which deal is better?

A £60 pair of trainers is on sale with “35% off”. A different shop sells the same trainers for £40. Which is cheaper?

To decide, you need to find 35% of £60. By the end of this lesson you will be able to do it in your head.

Step 2 · See it

Picture

See it as a bar

Percent means “out of 100”. Split the whole into 10 equal blocks and each block is 10%.

PercentageHow to find itOf £60
100%The whole amount£60
50%Halve it£30
10%Divide by 10£6
5%Halve 10%£3
1%Divide by 100£0.60

Step 3 · Understand how it works

Logic

Build it from blocks

Without a calculator, build any percentage from 50%, 10%, 5% and 1%.

35% = 10% + 10% + 10% + 5%.

With a calculator, use a multiplier: change the percentage into a decimal by dividing by 100, then multiply. 35% of £60 = 0.35 × 60.

Percent (%)
Out of 100.
Multiplier
The decimal you multiply by to find a percentage, e.g. 35% → 0.35.

Worked example

Find 35% of £60.

  1. 110% of £60 = £6.
  2. 230% = 3 × £6 = £18.
  3. 35% = half of 10% = £3.
  4. 435% = £18 + £3 = £21.

Answer: £21 off, so the trainers cost £39 — cheaper than £40.

Step 4 · Have a go

Do

Have a go

Do these without a calculator, then check with one.

  1. 120% of 80
  2. 215% of £40
  3. 375% of 120
  4. 412% of 250
  5. 5Challenge: what percentage of 80 is 28?

Step 5 · Remember it

Recall

Quick quiz

Use the building-block method.

0 of 4 answered

  1. 1.What is 10% of 350?

  2. 2.What is 25% of 48?

  3. 3.What is 15% of £80?

  4. 4.Which multiplier finds 7% of an amount?

Step 6 · Link it to your world

Reflect

Think about it

Percentages are in sales, interest rates, test scores and battery levels.

Where did you last see a percentage, and what did it tell you?

Saved to your notebook on this device only.

Finished all six steps?

Mark it complete to collect 3 stars. That's the last lesson in this course for now.