Year 9: Percentages

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1. What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The symbol for percent is %. For example, 50% means 50 out of 100, or 50 ÷ 100 = 0.5.

2. Converting Between Fractions, Decimals, and Percentages

• Fraction to Percentage: Multiply the fraction by 100 and add the % sign.
  Example: 3÷4 = 0.75 = 75%
• Decimal to Percentage: Multiply by 100.
  Example: 0.2 = 20%
• Percentage to Decimal: Divide by 100.
  Example: 65% = 0.65

3. Finding a Percentage of a Quantity

To find a percentage of a number, multiply the number by the percentage (as a decimal).

Formula: (percentage ÷ 100) × number

Example: 20% of 150 = 0.2 × 150 = 30

4. Increasing and Decreasing by a Percentage

• Increase: Multiply the number by (1 + percentage as a decimal)
  Example: Increase 200 by 10% ⇒ 200 × 1.10 = 220
• Decrease: Multiply the number by (1 − percentage as a decimal)
  Example: Decrease 150 by 20% ⇒ 150 × 0.80 = 120

5. Reverse Percentage Problems

To find the original amount before a percentage increase or decrease, divide by the multiplier.

Example: After a 25% increase, a shirt costs $75. What was the original price?

Solution: $75 ÷ 1.25 = $60

6. Percentage Change

To calculate percentage change:

Formula: (new value − original value) ÷ original value × 100%

Example: A phone goes from $600 to $720.
Change = 720 − 600 = 120
Percentage change = (120 ÷ 600) × 100% = 20%

7. Practice Questions

1. Convert 0.6 to a percentage.
2. Find 15% of 240.
3. Decrease 500 by 12%.
4. If a jacket is increased by 30% to $104, what was the original price?
5. A value increases from 200 to 260. What is the percentage increase?

8. Solutions

1. 0.6 × 100 = 60%
2. 0.15 × 240 = 36
3. 500 × 0.88 = 440
4. 104 ÷ 1.30 = 80
5. (260 − 200) ÷ 200 × 100 = 30%