Percentages

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Calculate a given percentage of a quantity
  2. Express one quantity as a percentage of another
  3. Calculate percentage increase or decrease
  4. Calculate with simple and compound interest
  5. Work with percentage calculations including: deposit, discount, profit and loss (as an amount or a percentage), earnings, and percentages over 100%
  6. Calculate using reverse percentages
  7. Solve problems involving repeated percentage change, such as finding the cost price when you know the selling price and percentage profit

1. Understanding Percentages

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What does "percentage" mean?

The word "percent" literally means "out of 100". When you see the % symbol, think of it as "/100". So 25% means 25 out of 100, which is the same as the fraction 25/100 or the decimal 0.25.

Why do we use percentages?

Percentages make it easier to compare different values. For example, which is bigger: 3/8 or 7/20? It's hard to tell. But if we convert them to percentages (37.5% and 35%), we can compare them instantly.

Converting between fractions, decimals, and percentages:

  • Fraction to percentage: Divide the top number by the bottom number, then multiply by 100

    • Example: 3/4 = 3 ÷ 4 = 0.75 = 0.75 × 100 = 75%

  • Decimal to percentage: Multiply by 100

    • Example: 0.36 = 0.36 × 100 = 36%

  • Percentage to decimal: Divide by 100

    • Example: 45% = 45 ÷ 100 = 0.45

  • Percentage to fraction: Write it over 100, then simplify

    • Example: 20% = 20/100 = 1/5

Common percentage equivalents to remember:

  • 50% = 1/2 = 0.5
  • 25% = 1/4 = 0.25
  • 75% = 3/4 = 0.75
  • 10% = 1/10 = 0.1
  • 1% = 1/100 = 0.01
  • 100% = 1 (the whole amount)

2. Calculating a Percentage of a Quantity

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This means finding a certain percentage of a number. For example, "What is 30% of 80?"

Method 1: Without a calculator (building blocks method)

Some percentages are easy to find:

  • 10% = divide by 10
  • 1% = divide by 100
  • 50% = divide by 2 (half the amount)
  • 25% = divide by 4 (quarter the amount)

You can use these as building blocks to find other percentages.

Example: Find 35% of 200

  • 10% of 200 = 200 ÷ 10 = 20
  • 30% of 200 = 20 × 3 = 60
  • 5% of 200 = 20 ÷ 2 = 10 (because 5% is half of 10%)
  • 35% of 200 = 60 + 10 = 70

Method 2: With a calculator (multiplier method)

A multiplier is the decimal version of a percentage. To find a percentage of a quantity, convert the percentage to a decimal and multiply.

Example: Find 12% of 650

  • Convert to decimal: 12% = 0.12
  • Multiply: 0.12 × 650 = 78

Percentages over 100%:

Sometimes you need to find percentages greater than 100%. Remember that 100% equals the original amount.

Example: Find 150% of 60

  • Method 1: 100% of 60 = 60, and 50% of 60 = 30, so 150% = 60 + 30 = 90
  • Method 2: Multiplier = 1.50, so 1.50 × 60 = 90

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