Percentage Increase and Decrease
Percentage increase and decrease use one formula: new value = original × (1 ± percentage change). Add to increase, subtract to decrease. A reverse percentage divides to find the original value.
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The Percentage Formula
- New value = original value × (1 ± percentage change)
- Use “+” for an increase, and “−” for a decrease
Calculating Percentage Increase and Decrease
- Increase: 60 increased by
- Decrease: 90 with
Finding the Original Value (Reverse Percentage)
- Use the same formula, but the original value is the unknown
- Solve it by dividing (e.g. original , so
Practice Questions
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A book costs £50. Its price increases by . What is the new price?
Correct! 🎉 +10 pointsNot quite right
Use the percentage increase formula: New Value = Original Value × (1 + Percentage Change). New £55.
A table originally cost £200, and it's now on sale for off. What's the sale price?
Correct! 🎉 +10 pointsNot quite right
Use the percentage decrease formula: New Value = Original Value × (1 − Percentage Change). New £140.
A cinema ticket costs £20. There's a student discount. What do you pay?
Correct! 🎉 +20 pointsNot quite right
Use the percentage decrease formula: New Value = Original Value × (1 − Percentage Change). New . Using the distributive law: and , so £17.
A game is advertised as " off" and now costs £60. What was the original price?
Correct! 🎉 +20 pointsNot quite right
Start with the formula: New Value = Original Value × (1 − Percentage Change). Plug in the values: Original Price × 0.75. To find the original price: £80.
A laptop originally cost £600. Its price increased by . What is the new price?
Correct! 🎉 +20 pointsNot quite right
Use the percentage increase formula: New Value = Original Value × (1 + Percentage Change). New . Using the distributive law: and , so £672.
A jacket is advertised as " off", and you also get an extra student discount on the reduced price. If the original price was £100, how much do you pay in total?
Correct! 🎉 +30 pointsNot quite right
Use the formula twice. First apply the discount: New £70. Then apply the student discount to £70: Final £63. Be careful not to subtract all at once.
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Students Also Ask
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The formula is original value × (1 plus or minus the percentage change) = new value. You add the percentage for an increase and subtract it for a decrease. First change the percentage to a decimal, then multiply the original value by this multiplier to find the new value.
To decrease a number by a percentage, subtract the percentage from 1 to build the multiplier. For example, a 30% decrease gives 1 - 0.3 = 0.7. Then multiply the original number by this multiplier. A £90 jacket with 30% off becomes 90 × 0.7 = £63.
First change the percentage to a decimal by dividing by 100, so 20% becomes 0.2. For an increase, add this decimal to 1, which gives 1.2. For a decrease, subtract it from 1 instead. Then multiply the original value by this multiplier to find the new value.
No, you do not need a new formula for reverse percentages. You use the same formula, put in the values you know, and solve it backwards. Instead of multiplying the original value by the multiplier, you divide the new value by the multiplier to find the original.
Build the multiplier by subtracting the discount from 1, so a 40% discount gives 0.6. Then divide the discounted price by this multiplier. For example, £36 paid after a 40% discount gives 36 ÷ 0.6 = £60. This reverses the discount to find the original price.