Grade 7 Percentages: Calculate Percentages, Discounts, Tax & Interest (US Standards)

GRADE 7 MATHEMATICS • LESSON 5

Percentages

النسبة المئوية

Understand “per hundred”, convert between percents, fractions and decimals, find a percent of a number, and work out increases and discounts — then take 15 exams with full step-by-step solutions.

What is a percent?

The word percent means “per hundred” — out of 100. The symbol is %. So 50% means 50 out of every 100, which is one half.

Picturing 100 equal squares makes it easy: a percent is simply how many of those 100 squares are shaded. Move the slider and watch.

🟪 Percent Grid (out of 100)
As a fraction
Simplified
As a decimal

Words you must know

Short, exact definitions to memorise.

Percent (%)
A number written as a part out of 100. 30% means 30 out of 100.
Percentage
The amount you get after taking a percent of something.
Percentage increase
When an amount grows. The new value is more than 100% of the original.
Percentage decrease / discount
When an amount shrinks. The new value is less than 100% of the original.

The same value, three ways

A percent, a fraction and a decimal can all describe the same amount.

Examples:   25% = 25/100 = 1/4 = 0.25   •   50% = 1/2 = 0.5   •   10% = 1/10 = 0.1

Working with percentages

Your main study reference. Every method is broken into numbered steps, each one explained, with a worked example and a teacher hack.

1) Converting: percent ↔ fraction ↔ decimal

  1. Percent to fraction: write the number over 100, then simplify. 40% = 40/100 = 2/5.
  2. Percent to decimal: divide by 100 (move the point two places left). 40% = 0.40 = 0.4.
  3. Decimal to percent: multiply by 100 (move the point two places right). 0.7 = 70%.
Hack: the % sign is a shortcut for “÷ 100”. Removing it means dividing by 100; adding it means multiplying by 100.

2) Finding a percent of a number

  1. Turn the percent into a fraction of 100. X% means X out of 100.
  2. The word “of” means multiply. So X% of N = N × X, then ÷ 100.
  3. Do the arithmetic. Multiply first, then divide by 100.
Example: 15% of 80
80 × 15 = 1200
1200 ÷ 100 = 12
Hack — the 10% trick: 10% of a number is just ÷ 10. Then build others: 5% is half of 10%, 20% is double 10%, and 15% = 10% + 5%.

3) Percentage increase

  1. Find the extra part. Work out the percent of the original amount.
  2. Add it on. New amount = original + the extra part.
Example: increase 200 by 15%
15% of 200 = 30
200 + 30 = 230
Hack: increasing by 15% is the same as finding 115% of the amount in one step.

4) Percentage decrease (discount)

  1. Find the part to remove. Work out the percent of the original amount.
  2. Subtract it. New amount = original − that part.
Example: a 30 item with 20% off
20% of 30 = 6
30 − 6 = 24
Hack: taking 20% off is the same as paying 80% of the price in one step.

5) What percent is one number of another

  1. Compare the two numbers. Write the part out of the whole.
  2. Multiply by 100. This turns the comparison into a percent.
Example: 18 out of 24 is what percent?
(18 × 100) ÷ 24 = 1800 ÷ 24
= 75%
Hack: “part ÷ whole × 100” always gives the percent.

6) Finding the whole (reverse percent)

  1. Know what you have. You are told that X% of the whole equals a value V.
  2. Work back to 100%. Multiply V by 100 and divide by X.
Example: 20% of a number is 30. Find the number.
(30 × 100) ÷ 20 = 3000 ÷ 20
= 150
Hack: find 1% first (V ÷ X), then 100% is that × 100.
🧮 Percent Calculator

Test Yourself — 15 Exams

Each exam has 10 questions, and every answer comes with a step-by-step solution — even when you get it right.

Key takeaways

1. Percent means “out of 100”. The % sign is a shortcut for ÷ 100.

2. To find a percent of a number: multiply by the percent, then divide by 100.

3. Increase = original + the part; decrease = original − the part.

4. “What percent”: part ÷ whole × 100.

5. 10% is just ÷ 10 — build 5%, 20% and 15% from it for fast mental maths.