Percentages of Amounts and Percentage Change
Percentages of amounts and percentage change covers finding a percentage of a quantity, since a percentage is a fraction out of 100, so finding 23% of an amount is equivalent to finding 23/100 of it, or multiplying by the decimal 0.23. Percentage change problems use a multiplier, with an increase of a given percentage multiplying the original amount by (1 + the percentage as a decimal) and a decrease multiplying it by (1 - the percentage as a decimal).
Before you start
Make sure you're comfortable with these topics first:
Method
- To find 1% of an amount, divide by 100; scale this up by multiplying by the number of percent you need (for example, find 1% then multiply by 23 to find 23%).
- Non-calculator building-block method: find 10% by dividing by 10, then find 5% by halving the 10% value, and 1% by dividing the 10% value by 10, then add combinations of these to make the percentage asked for.
- Calculator method: convert the percentage to a decimal multiplier by dividing by 100 (for example 23% = 0.23), then multiply the decimal multiplier by the amount.
- For a percentage increase, find the multiplier by adding the percentage (as a decimal) to 1 (for example a 15% increase uses the multiplier 1.15), then multiply the original amount by this multiplier.
- For a percentage decrease, find the multiplier by subtracting the percentage (as a decimal) from 1 (for example a 15% decrease uses the multiplier 0.85), then multiply the original amount by this multiplier.
- To find a percentage change from an original value to a new value, calculate (change / original) x 100; a positive result is a percentage increase and a negative result is a percentage decrease.
- Read the question carefully to decide whether it wants the new amount after the change (use the multiplier method) or the percentage change itself (use the change / original x 100 method).
Worked example
A laptop's normal price is 640 pounds. In a sale it is reduced to 480 pounds. Calculate the percentage decrease in price.
- Find the decrease in price: 640 - 480 = 160 pounds.
- Divide the decrease by the ORIGINAL price (not the new price): 160 / 640.
- Work out 160 / 640 = 0.25.
- Convert to a percentage by multiplying by 100: 0.25 x 100 = 25%.
Practice questions
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Q1Find 15% of 260 pounds.Show answer
Answer: 39 pounds
Q2Find 8% of 350 kg.Show answer
Answer: 28 kg
Q3A games console costs 72 pounds. Its price is increased by 25% ahead of a busy shopping period. Work out the new price.Show answer
Answer: 90 pounds
Q4A winter coat costs 156 pounds. It is decreased by 30% in a January sale. Work out the sale price.Show answer
Answer: 109.20 pounds
Q5A monthly train season ticket rises from 95 pounds to 115.90 pounds. Calculate the percentage increase.Show answer
Answer: 22%
Q6A village's population falls from 2400 to 2160. Calculate the percentage decrease.Show answer
Answer: 10%
Q7Explain why dividing an amount by 100 and then multiplying by 40 gives 40% of the amount.Show answer
Answer: Dividing by 100 finds 1% of the amount (one hundredth), and multiplying this by 40 scales it up to 40 lots of 1%, which is exactly 40% of the original amount.
Q8A meal out costs 54 pounds before a service charge. A 12.5% service charge is added. Work out the total cost including the service charge.Show answer
Answer: 60.75 pounds
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A washing machine has a normal price of 380 pounds. It is reduced by 35% in a sale. Calculate the sale price.
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Deepak's weekly wage increases from 480 pounds to 540 pounds. (a) Calculate the percentage increase in his wage. (b) Deepak claims his wage has 'gone up by more than an eighth'. Is Deepak correct? Justify your answer by comparing your percentage to 1/8 written as a percentage.
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After the number of pupils at a school increases by 15%, the school now has 690 pupils. Work out how many pupils the school had before the increase.
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Free printable worksheet
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This topic is chapter 11 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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