Lesson 6. Percentages

Fractions and percentages.

Per cent means ‘out of 100’. Percentages are fractions with denominator (bottom number) equal to 100.

EXAMPLES:

63% means ⁶³/₁₀₀

7% means ⁷/₁₀₀.

17 out of 100 small squares are shaded.

Fraction shaded = ¹⁷/₁₀₀

Percentage shaded = 17%.

Changing percentages into fractions.

EXAMPLES:

41% = ⁴¹/₁₀₀

Changing fractions into percentages.

EXAMPLES:

To change a fraction into a percentage, multiply the fraction by 100.

(to the nearest whole number)

Percentage of a number.

Common percentages.

50% = ¹/₂    25% = ¹/₄    75% = ³/₄    

33¹/₃% = ¹/₃    66²/₃% = ²/₃

EXAMPLES:

25% of 60 = ¹/₄ × 60 = 60 ÷ 4 = 15.

75% of 36 = ³/₄ × 36 = (36 ÷ 4) × 3 = 27.

66²/₃% of 24 = ²/₃ × 24 = (24 ÷ 3) × 2 = 16.

Multiples of 10%

10% = ¹/₁₀

To work out 20%, find 10% then multiply by 2.

To work out 30%, find 10% then multiply by 3 and so on.

Harder percentage.

To find 1% of a number, divide the number by 100.

EXAMPLES:

Find 23% of a number. Divide the number by 100 to find 1% then multiply by 23 to find 23% of the number.

Find 12% of 2300

1% of 2300 = 2300 ÷ 100

12% of 2300

= (2300 ÷ 100) × 12 = 276

Percentages and decimals.

EXAMPLES:

NOTE

To change decimals into percentages, the first two numbers after the point give the percent:

NOTE

Tasks to the lesson 6

• Test 1
• Test 2
• Test 3

Other lessons:

• Lesson 1. Patio
• Lesson 3. Direct proportion
• Lesson 5. Sharing in a given ratio
• Lesson 7. Percentage of a number
• Lesson 9. Percentage change
• Lesson 10. Compound interest-type problems
• Lesson 11. Tasks for a time