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Percentages — Study Notes & Practice Pack

Percentages — Student Success Notes & Practice Pack

Clear rules, worked examples and practice questions.

1. Converting Between Fractions, Decimals & Percentages

Percent means "per 100". Convert by multiplying/dividing by 100 as needed.

Examples
  1. 45/60 × 100 = 75%
  2. 0.65 × 100 = 65%
  3. 87% ÷ 100 = 0.87
Practice (3)
  1. Write 9/20 as a percentage.
  2. Convert 0.725 to a percentage.
  3. Write 135% as a decimal.

2. Finding a Percentage of a Quantity

Use percentage/100 × amount.

Examples
  1. 20% of 150 = 0.20 × 150 = 30
  2. 8% of 140 = 0.08 × 140 = 11.2
  3. 15% of $240 = 0.15 × 240 = 36
Practice (3)
  1. Find 25% of 60.
  2. Find 12% of 320.
  3. A shop has 480 apples. Find 7.5% of them.

3. Expressing One Quantity as a Percentage of Another

Use (part/whole) × 100%.

Examples
  1. 12/48 × 100 = 25%
  2. 1.92/1.60 × 100 = 120%
  3. 268/604 × 100 ≈ 44.37%
Practice (3)
  1. Express 30 as a percentage of 50.
  2. A bag contains 45 red marbles out of 60. Find the % red.
  3. Write $6.50 as a % of $13.

4. Percentage Increase or Decrease

Increase: new = original × (1 + %/100). Decrease: new = original × (1 - %/100).

Examples
  1. 120 × 1.15 = 138 (15% increase)
  2. 520 × 0.85 = 442 (15% decrease)
  3. 3500 × 0.88 = 3080 (12% decrease)
Practice (3)
  1. Increase $90 by 8%.
  2. Decrease 250 by 15%.
  3. A bike worth $480 is reduced by 22%. Find new price.

5. Reverse Percentage Problems

Use original = final ÷ (1 ± %/100).

Examples
  1. 240 ÷ 1.20 = 200 (20% increase)
  2. 85 ÷ 0.85 = 100 (15% decrease)
  3. 37054 ÷ 0.955 ≈ 38800 (4.5% decrease)
Practice (3)
  1. After a 25% increase, a phone costs $750. Find original price.
  2. After a 10% discount, a jacket costs $72. Find original price.
  3. Population after 5% decrease is 2850. Find original population.

6. Simple Interest

Formula: I = (P × r × t) / 100.

Examples
  1. P=8500, r=1.7%, t=4 → I=578
  2. P=600, r=1.5%, t=7 → I=63
  3. P=500, r=2%, t=15 → I=150
Practice (3)
  1. Find simple interest on $4000 at 3% for 2 years.
  2. $1200 at 2.5% for 4 years, find interest.
  3. $750 at 1.8% for 5 years, find total amount.

7. Compound Interest

Formula: Total = P × (1 + r/100)^t.

Examples
  1. 1000 × 1.04^2 = 1081.60
  2. 2500 × 1.03^4 ≈ 2819.08
  3. 200 × (1.000035)^365 ≈ 202.57
Practice (3)
  1. Value of $1000 after 2 years at 4% compound interest.
  2. $2500 at 3% for 4 years: total?
  3. $150 at 0.5% per day for 30 days: value?

8. Profit & Loss Percentage

Profit% = (profit / cost price) × 100. Loss% similar.

Examples
  1. Buy 2.50, sell 4.20 → 68% profit
  2. Buy 5.00, sell 4.60 → 8% loss
  3. Buy 40, sell 45.40 → 13.5% profit
Practice (3)
  1. Buy $80, sell $96. Profit %?
  2. Buy $50, sell $42. Loss %?
  3. Buy $3.50, sell $4.20. Profit %?

9. Percentage in Context Problems

These combine percentages with rates, units or ratios — do step-by-step.

Examples
  1. Ferry: 80% of 600 × 2h = 960; 65% of 600 × 3h = 1170 → total 2130
  2. Potatoes: 18% of 1200 = 216; 25% = 300 → remaining = 684
  3. Pool: 72% of 5000 L = 3600 L
Practice (3)
  1. A bus takes 80 passengers full. It runs 80% full for 3 trips and 50% full for 2 trips. How many passengers?
  2. A warehouse has 2000 boxes. 12% are dispatched, 8% returned. How many left?
  3. A 700 g fruit is 87% water. What mass is water?

10. Exam Tips

Underline key words. Convert units. Round only at the end. Use brackets in calculators. Estimate to check answers.

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