Percentage Increase and Decrease
Learn how to calculate percentage increase and decrease using the formula: original value × (1 ± percentage change). Let's get started! 🚀
Video Lesson
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Flashcards
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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 20% = 60 × (1 + 20%) = 60 × 1.2 = 72
- Decrease: 90 with 30% off = 90 × (1 − 30%) = 90 × 0.7 = 63
🛎️ Finding the Original Value (Reverse Percentage)
- Use the same formula, but the original value is the unknown
- Solve it by dividing (e.g. original × 0.6 = 36, so original = 36 ÷ 0.6 = 60)
Practice Questions
Test your understanding
A book costs £50. Its price increases by 10%. What is the new price?
Correct! 🎉 +10 pointsNot quite right
Use the percentage increase formula: New Value = Original Value × (1 + Percentage Change). New Price = 50 × (1 + 0.10) = 50 × 1.1 = £55.
A table originally cost £200, and it's now on sale for 30% off. What's the sale price?
Correct! 🎉 +10 pointsNot quite right
Use the percentage decrease formula: New Value = Original Value × (1 − Percentage Change). New Price = 200 × (1 − 0.30) = 200 × 0.7 = £140.
A cinema ticket costs £20. There's a 15% student discount. What do you pay?
Correct! 🎉 +20 pointsNot quite right
Use the percentage decrease formula: New Value = Original Value × (1 − Percentage Change). New Price = 20 × (1 − 0.15). Using the distributive law: 20 × 1 = 20 and 20 × 0.15 = 3, so 20 − 3 = £17.
A game is advertised as "25% 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: 60 = Original Price × 0.75. To find the original price: 60 ÷ 0.75 = £80.
A laptop originally cost £600. Its price increased by 12%. What is the new price?
Correct! 🎉 +20 pointsNot quite right
Use the percentage increase formula: New Value = Original Value × (1 + Percentage Change). New Price = 600 × (1 + 0.12). Using the distributive law: 600 × 1 = 600 and 600 × 0.12 = 72, so 600 + 72 = £672.
A jacket is advertised as "30% off", and you also get an extra 10% 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 30% discount: New Price = 100 × (1 − 0.30) = £70. Then apply the 10% student discount to £70: Final Price = 70 × (1 − 0.10) = £63. Be careful not to subtract 40% all at once.
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