All skills Math

Learn Index · Fractions, Decimals, and Percentages Grade 9–10

Real-world percentage problems

Using percents in situations like sales, surveys and growth.

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Percents in the real world

Percents describe sales, taxes, tips, interest, grades, statistics, nutrition labels and more. Most problems use one of three questions, and the key is spotting which one.

The three percent questions

Question Example Method
Find the part What is 15% of 80? 0.15 × 80 = 12
Find the percent 12 is what percent of 80? 12 ÷ 80 = 0.15 = 15%
Find the whole 12 is 15% of what? 12 ÷ 0.15 = 80

All three come from: part = percent × base. The base is the whole the percent is taken of.

Shopping

Discount + tax: A $75 game is 20% off, then 13% HST.

75 × 0.80 × 1.13 = $67.80

Business: markup and profit

A store buys a lamp for $40 and applies a 75% markup on cost.

Selling price = 40 × 1.75 = $70. Profit = $30.

Earnings: commission

A salesperson earns 6% commission. Sales of $18,500 → 0.06 × 18,500 = $1,110.

Money: simple interest

Interest = principal × rate × time.

$2,000 at 3% per year for 4 years: 2,000 × 0.03 × 4 = $240.

Nutrition labels

A granola bar has 4 g of fibre, which is 14% of the daily value. What is the daily value?

4 ÷ 0.14 ≈ 28.6 g.

Grades

You scored 42 out of 50. Percent = 42 ÷ 50 = 84%.

You need 80% on a test out of 60. Marks needed = 0.80 × 60 = 48.

Statistics and surveys

In a survey, 360 of 1,200 people prefer cycling. Percent = 360 ÷ 1,200 = 30%.

If 30% of a city of 450,000 feel the same, that’s about 135,000 people.

Reverse problems

Example: A shirt costs $33.90 including 13% tax. Price before tax?

33.90 ÷ 1.13 = $30.

Worked examples

Example 1: A $640 rent rises 2.5%. New rent?

640 × 1.025 = $656.

Example 2: A team won 27 of 45 games. Win percentage?

27 ÷ 45 = 60%.

Example 3: A 25% tip was $9. What was the bill?

9 ÷ 0.25 = $36.

Common mistakes

  • Using the wrong base (e.g., taking a percent of the final price instead of the original).
  • Subtracting tax to undo it instead of dividing by 1.13.
  • Mixing up "percent of" and "percent more than".

Try it yourself

  1. 35% of 240
  2. 18 is what percent of 72?
  3. 45 is 60% of what number?
  4. A $120 bike is marked up 40%. Selling price?
  5. A total of $56.50 includes 13% tax. Pre-tax price?

Answers: 1) 84 2) 25% 3) 75 4) $168 5) $50

Quick recap

  • Part = percent × base: solve for whichever is missing.
  • Percents run through shopping, markup, commission and interest.
  • Undo a percent increase by dividing, not subtracting.