Percentage change and original values
Percentage change questions are everywhere: sale prices, wage rises, interest and population growth. The reliable method is always the multiplier.
Part of your national curriculum
- Ratio, proportion and rates of change: Solve problems involving percentage change, including percentage increase and decrease and original value problems
Lesson overview
What you'll learn in this lesson
Solve problems involving percentage change, including percentage increase and decrease and original value problems
Key learning points
- • Change as a proportion of the original
- • Increase and decrease multipliers
- • Reverse percentages
- • Simple and compound
This lesson at a glance
- 30 minutes
- 21 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 21
Visual introductionPicture this
Percentage change and original values
Percentage change questions are everywhere: sale prices, wage rises, interest and population growth. The reliable method is always the multiplier.
In a nutshell
Solve problems involving percentage change, including percentage increase and decrease and original value problems
Learning cycle
Part 2 of 21
Learning cycle 1 of 2
Part 1 · Change as a proportion of the original
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 21
Learn
Change as a proportion of the original
Percentage change is the change divided by the original amount, multiplied by 100. A rise from £40 to £46 is a change of £6 on an original of £40, which is 15%. Dividing by the new amount instead of the original is the most common mistake.
Reset break
Part 4 of 21
Pause
That's sitting 1 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 21
Learn
Increase and decrease multipliers
A 15% increase multiplies by 1.15; a 15% decrease multiplies by 0.85. One multiplication replaces two steps and works just as well for repeated change: three years of 4% growth is × 1.04³.
Quick check
Part 6 of 21
Quick check
Part 7 of 21
Reset break
Part 8 of 21
Pause
That's sitting 2 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 21
Learning cycle 2 of 2
Part 2 · Reverse percentages
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 21
Learn
Reverse percentages
If a jacket costs £68 after a 15% reduction, the £68 represents 85% of the original. Dividing by 0.85 gives £80. Adding 15% back to £68 gives £78.20, which is wrong, because the 15% was calculated on the larger original price.
Explore the idea
Part 11 of 21
Learn
Simple and compound
Simple interest adds the same amount each year; compound interest adds a percentage of the growing balance. £2,000 at 3.5% for four years gives £2,280 simple but 2000 × 1.035⁴ = £2,295.02 compound, and the gap widens with time.
Reset break
Part 12 of 21
Pause
That's sitting 3 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 13 of 21
Quick check
Part 14 of 21
Explore the idea
Part 15 of 21
Worked example
Worked answer: after a 15% reduction a coat costs £68. Find the original price (3 marks)
The sale price represents 100% − 15% = 85% of the original (1). The multiplier is therefore 0.85, so the original is 68 ÷ 0.85 (1), which equals £80 (1). Checking: 15% of £80 is £12, and £80 − £12 = £68.
Reset break
Part 16 of 21
Pause
That's sitting 4 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 17 of 21
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 18 of 21
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ change is the change divided by the original amount, multiplied by 100.
A rise from £40 to £46 is a ____ of £6 on an original of £40, which is 15%.
A 15% ____ multiplies by 1.15; a 15% decrease multiplies by 0.85.
Challenge round
Part 19 of 21
Game · Recall cards
Increase 240 by 15%.
Card 1 of 4
Mastery quiz
Part 20 of 21
Marked quiz
End of lesson quiz: Percentage change and original values
4 questions, marked with the reasoning shown. No timer.
1. Increase 240 by 15%.
2. A count drops from 200 to 150. The percentage decrease is…
3. Which multiplier applies a 7% decrease?
4. 620 gorillas rise to 1,020. The increase is about…
Lesson round-up
Part 21 of 21
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 21 · Watch & discover
How this is going
- Not looked at yet
Solve problems involving percentage change, including percentage increase and decrease and original value problems