Percentage Change and Multipliers
A percentage multiplier is a single decimal that increases or decreases an amount by a percentage in one calculation, instead of finding the percentage separately and then adding or subtracting it. Percentage change measures how much a value has grown or shrunk compared with where it started, found by dividing the change in value by the original value and multiplying by 100, and dividing a new amount by its multiplier finds the original amount before the change.
Before you start
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Method
- To increase by a percentage, write the multiplier as 1 plus the percentage as a decimal (for example, an increase of 8% has multiplier 1.08).
- To decrease by a percentage, write the multiplier as 1 minus the percentage as a decimal (for example, a decrease of 15% has multiplier 0.85).
- Multiply the original amount by the multiplier to find the new amount, in one calculation.
- To find a percentage change from an original value to a new value, find the difference (new minus original), divide this difference by the original value, then multiply by 100.
- A positive percentage change is an increase; if the difference comes out negative, the value has decreased.
- To find an original amount before a known percentage change (a reverse percentage problem), divide the new amount by the multiplier - do not try to add or subtract a percentage of the new amount.
- Applying two percentage changes one after another is not the same as adding the percentages together - work out and apply each multiplier in turn, using the previous answer each time.
Worked example
A laptop originally costs 640 pounds. In a sale, the price is reduced by 12%, and then a loyalty card gives a further 5% off the new, already-reduced, price. Work out the final price of the laptop.
- Find the multiplier for a 12% decrease: 1 - 0.12 = 0.88.
- Apply it to the original price: 640 x 0.88 = 563.20 pounds.
- Find the multiplier for the further 5% decrease: 1 - 0.05 = 0.95.
- Apply this second multiplier to the new price, not the original price: 563.20 x 0.95 = 535.04 pounds.
- The final price of the laptop is 535.04 pounds.
Practice questions
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Q1Increase 250 pounds by 6%, using a multiplier.Show answer
Answer: 265 pounds (250 x 1.06)
Q2Decrease 84 kg by 25%, using a multiplier.Show answer
Answer: 63 kg (84 x 0.75)
Q3A car's value falls from 14000 pounds to 11900 pounds over one year. Work out the percentage decrease in its value.Show answer
Answer: 15% (difference = 2100, then 2100 / 14000 x 100)
Q4A phone bill rises from 32 pounds a month to 34.56 pounds a month. Work out the percentage increase.Show answer
Answer: 8% (difference = 2.56, then 2.56 / 32 x 100)
Q5After a 20% pay rise, Tunde's hourly wage is now 13.20 pounds. Work out his hourly wage before the rise.Show answer
Answer: 11 pounds (13.20 / 1.20)
Q6A jacket's price is reduced by 30% in a sale to 42 pounds. Work out the jacket's original price.Show answer
Answer: 60 pounds (42 / 0.70)
Q7A charity's annual donations increase by 4% one year, then by a further 4% the next year, starting from 50000 pounds. Work out the total donations after these two years of growth.Show answer
Answer: 54080 pounds (50000 x 1.04 x 1.04)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A gym membership costs 45 pounds per month. The gym increases all membership prices by 8%, and then, six months later, increases the new price by a further 2.5%. Work out the monthly membership price after both increases, giving your answer to the nearest penny.
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A company's website traffic falls by 35% in January, compared with December, to 5850 visitors. (a) Work out how many visitors the website had in December. (b) In February, traffic then rises by 20% compared with January. Work out the number of visitors in February.
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Free printable worksheet
Want more practice on paper? Download the percentage change and multipliers worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 40 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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