Percentage Increases & Decreases (Cambridge International IGCSE Maths)

Percentage increases & decreases

How do I increase by a percentage?

• A percentage increase makes an amount bigger by adding that percentage on to itself

• Without a calculator, use the the basic percentages methods to find the percentage you are increasing by

  • Then add this on to the original amount

  • To increase 30 by 10%

    • 10% of 30 is 3
    • 30 + 3 = 33
    • This is equivalent to finding 110% of 30

• With a calculator it is more efficient to use multipliers

  • A multiplier is the decimal equivalent of a percentage

    • A percentage can be converted to a decimal by dividing by 100

  • When increasing by a percentage, we are finding a percentage greater than 100%

  • To increase 80 by 15%

    • We are finding 115% of 80, so the multiplier is 1.15
    • 1.15 × 80 = 92

How do I decrease by a percentage?

• A percentage decrease makes an amount smaller by subtracting that percentage from itself

• Without a calculator, use the methods outlined in Basic Percentages to find the percentage you are decreasing by

  • Then subtract this from the original amount

  • To decrease 30 by 10%

    • 10% of 30 is 3

    • 30 - 3 = 27

    • This is equivalent to finding 90% of 30

      • Because 100% - 10% = 90%

• With a calculator it is more efficient to use multipliers

  • When decreasing by a percentage, we are finding a percentage smaller than 100%

  • To decrease 80 by 15%

    • We are finding 85% of 80, so the multiplier is 0.85

      • Because 100% - 15% = 85%

    • 0.85 × 80 = 68

Worked Example (a) Increase 200 kg by 21%.

Answer:

Method 1 (non-calculator)

By first finding 10% and 1%, find 21% of 200

10% of 200 = 20 1% of 200 = 2 21% of 200 = 20 + 20 + 2 = 42

Add this to the original amount

200 + 42

Final answer: 242 kg

Method 2 (calculator)

An increase by 21% is equivalent to finding 121% of the original amount So the multiplier is 1.21

1.21 × 200

Final answer: 242 kg

(b) An item that costs £500 is discounted by 35%.

Find the new price of the item.

Answer:

A discount of 35% means the price decreases by 35%

Method 1 (non-calculator)

By first finding 10% and 5%, find 35% of 500

10% of 500 = 50 5% of 500 = 25 35% of 500 = 50 + 50 + 50 + 25 = 175

Subtract this from the original amount

500 - 175

Final answer: £325

Method 2 (calculator)

A decrease of 35% is equivalent to finding 65% of the original amount (100 - 35 = 65) So the multiplier is 0.65

500 × 0.65

£325