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GRADES 6–7 · MATHEMATICS

Understanding Percentages

Percentages are used in shopping, scores, surveys, discounts and many everyday situations. Learn what “per cent” means, how percentages connect to fractions and decimals, and how to calculate a percentage of an amount.

Learning time: approximately 30 minutes · Beginner level

What You Will Learn

1. What Does Percent Mean?

The word percent means “per hundred” or “out of 100”. The symbol is %.

25100=25%

25% means 25 out of every 100 equal parts.

100% represents one whole. 50% represents one half. 0% represents none of the whole.

2. Connect Percentages and Fractions

To write a percentage as a fraction, put the number over 100 and simplify if possible.

PercentageFraction out of 100Simplified fraction
50%50/1001/2
25%25/1001/4
75%75/1003/4
20%20/1001/5
10%10/1001/10
Example: 40% = 40/100. Divide the numerator and denominator by 20 to get 2/5.

3. Convert a Percentage to a Decimal

To convert a percentage to a decimal, divide by 100. A quick way is to move the decimal point two places to the left.

Why does 8% become 0.08? Eight per cent means 8/100, which is eight hundredths, or 0.08.

4. Convert a Decimal to a Percentage

To convert a decimal to a percentage, multiply by 100. Move the decimal point two places to the right and add the percent symbol.

Do not mix up the directions: Percent to decimal means divide by 100. Decimal to percent means multiply by 100.

5. Find a Percentage of an Amount

Convert the percentage to a decimal, then multiply by the amount. For common percentages, you can also use familiar fractions.

Worked example: Find 20% of 60

  1. Convert 20% to a decimal: 0.20.
  2. Multiply: 0.20 × 60 = 12.

Answer: 12.

Another example: Find 15% of 80

Convert 15% to 0.15. Then 0.15 × 80 = 12.

Quick method for 10%: Divide an amount by 10. For example, 10% of 70 is 7. To find 20%, double the 10% amount: 14.

6. Solve Everyday Problems

Example 1: A test score

A student answers 18 questions correctly out of 20. What percentage is correct?

18/20 × 100% = 90%. The student scores 90%.

Example 2: A discount

A bag costs $50 and has a 10% discount. How much money is taken off?

10% of $50 = 0.10 × 50 = $5 discount. The new price is $50 − $5 = $45.

Example 3: A class survey

There are 30 students in a class. If 40% choose football as their favourite sport, how many students is that?

40% of 30 = 0.40 × 30 = 12 students.

7. Common Mistakes to Avoid

Forgetting “out of 100”: 35% means 35/100, not 35 whole units.
Moving the decimal the wrong way: Divide by 100 for percent-to-decimal; multiply by 100 for decimal-to-percent.
Confusing percentage points and amounts: A 10% discount on $50 is $5, not $10.
Assuming every percentage is below 100%: 125% is possible and means 1.25 times the original amount.

8. Practice Exercises

Try these before revealing the answers.

  1. Write 35% as a fraction over 100.
  2. Convert 60% to a decimal.
  3. Convert 0.45 to a percentage.
  4. Find 25% of 80.
  5. Find 15% of 200.
  6. A learner gets 16 out of 20 questions correct. What percentage is correct?
  7. A $40 item is reduced by 25%. Find the discount and the new price.
Show practice answers and working
  1. 35/100 = 7/20 in simplest form.
  2. 0.60 or 0.6.
  3. 45%.
  4. 0.25 × 80 = 20.
  5. 0.15 × 200 = 30.
  6. 16/20 × 100% = 80%.
  7. 25% of $40 is $10. New price = $40 − $10 = $30.

9. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. What does 25% mean?
2. What is 40% as a decimal?
3. What is 0.75 as a percentage?
4. What is 10% of 90?
5. A student gets 15 out of 20 correct. What is the score as a percentage?

10. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grades 6–7 Mathematics

Understanding Percentages Worksheet

Name: __________________________ Date: _______________

Instructions: Show your working where needed.

  1. Write 45% as a fraction over 100 and simplify.
  2. Convert 7% to a decimal.
  3. Convert 0.32 to a percentage.
  4. Find 50% of 86.
  5. Find 15% of 60.
  6. A team wins 12 of its 15 games. What percentage of games does it win?
  7. A $80 jacket is discounted by 20%. Find the discount and sale price.

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 45/100 = 9/20.
  2. 0.07.
  3. 32%.
  4. 43.
  5. 0.15 × 60 = 9.
  6. 12/15 × 100% = 80%.
  7. 20% of $80 = $16 discount; sale price = $64.

11. Lesson Summary

Next learning goal: Apply percentages to percentage increase and decrease, discounts and more challenging real-life problems.

Educational note: This is a curriculum-neutral lesson for Grades 6–7. Teachers and parents can adapt examples and practice to their local curriculum.