Number
Grade 4-5Percentage Increase & Decrease
Percentage increase and decrease questions ask for the new amount after a change, not just the size of the change itself, and that distinction is where most marks are lost. This lesson covers increasing and decreasing amounts using the 10% and 5% building-block method, and using a decimal multiplier with a calculator.
What you need to know
- Percentage change is the change divided by the original amount, times 100.
- To increase by 12%, multiply by 1.12; to decrease by 12%, multiply by 0.88.
- The multiplier is 1 plus rate/100 for a rise, 1 minus rate/100 for a fall.
- Profit and loss percentages are worked out on the cost price, not the selling price.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Increasing an amount without a calculator
Find the percentage using the 10%/5% building-block method, then add it to the original amount to get the new, larger amount.
Increase £80 by 15%: 10% of £80 is £8, and 5% is half of that, £4. Adding these gives 15% = £12. Add this to the original amount: £80 + £12 = £92.
Decreasing an amount without a calculator
Find the percentage in the same way, then subtract it from the original amount to get the new, smaller amount.
Decrease £90 by 20%: 10% of £90 is £9, so 20% is £18. Subtract this from the original amount: £90 - £18 = £72.
Using a decimal multiplier with a calculator
For an increase, add the percentage to 100% and convert the total to a decimal, then multiply directly by the original amount. For a decrease, subtract the percentage from 100% instead.
Increase £350 by 8%: 100% + 8% = 108%, which is 1.08 as a decimal. Multiply: 1.08 × 350 = £378. Decrease £420 by 15%: 100% - 15% = 85%, which is 0.85. Multiply: 0.85 × 420 = £357.
Percentage change in real-world problems
Word problems describe percentage changes using everyday language: a sale, a pay rise, or a fall in value all signal an increase or decrease to apply to a starting amount. Always give the new amount as the final answer, not just the size of the change.
A car bought for £12,000 that decreases in value by 18% is worth 0.82 × 12,000 = £9840 after one year, not £2160, which is only the amount lost.
Worked examples
Three exam-style questions, fully solved
Increase £80 by 15%.
Easy- 1.Find 10% of £80 by dividing by 10: £8
- 2.Find 5% of £80 by halving the 10% value: £4
- 3.Add the percentage found to the original amount: £80 + £8 + £4
Answer: £92
A jacket normally costs £64. In a sale, the price is reduced by 25%. What is the sale price?
Medium- 1.Recognise that a reduction means subtracting the percentage from 100%: 100% - 25% = 75%
- 2.Convert 75% to a decimal: 0.75
- 3.Multiply the decimal by the original price: 0.75 × 64
Answer: £48
A car is bought for £12,000. After one year, its value has decreased by 18%. What is the car's value after one year?
Hard- 1.Recognise that a decrease means subtracting the percentage from 100%: 100% - 18% = 82%
- 2.Convert 82% to a decimal: 0.82
- 3.Multiply the decimal by the original value: 0.82 × 12,000
Answer: £9840
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
A price rises from £40 to £50. What is the percentage increase?
A population falls from 800 to 600. What is the percentage decrease?
Increase 60 by 20%.
Decrease 250 by 12%.
A house bought for £200 000 is sold for £260 000. What is the percentage profit?
A club grows from 45 members to 54 members. What is the percentage increase?
Avoid these
The mistakes students make most often
Working out the percentage of the amount and giving that as the final answer, instead of adding it to or subtracting it from the original amount.
Using a decimal multiplier greater than 1 for a decrease, or less than 1 for an increase, for example using 0.85 by mistake when the amount should increase.
When using the 10%/5% method, recalculating 5% from scratch instead of halving the 10% value already found.
Leaving the units off the final answer, for example writing 92 instead of £92.
Misreading "increase by 15%" as adding a flat amount of 15, rather than 15% of the original value.
FAQ
Questions students and parents ask
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What to learn next
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