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GRADE 6 · MATHEMATICS

Equivalent Fractions

Discover how fractions with different numbers can represent exactly the same amount. Use visual models, learn the multiplication rule and practise simplifying fractions.

Learning time: approximately 20–25 minutes · Beginner level

What You Will Learn

1. What Are Equivalent Fractions?

Equivalent fractions are fractions that have different numerators or denominators but represent the same value.

For example, 1/2, 2/4 and 3/6 all represent one half.

Each bar shows the same shaded amount: one half.
1/2
2/4
3/6

The pieces are divided differently, but the shaded part is equal in every bar.

2. Make Equivalent Fractions by Multiplying

To make an equivalent fraction, multiply the numerator and denominator by the same non-zero number.

Example: Start with 2/3

  1. Multiply the numerator and denominator by 2.
  2. Numerator: 2 × 2 = 4.
  3. Denominator: 3 × 2 = 6.
  4. So 2/3 = 4/6.
Remember: Whatever you do to the numerator, do the same to the denominator. Multiplying only one of them changes the value.

More examples:

3. Simplify Fractions by Dividing

Simplifying means writing a fraction with smaller numbers while keeping the same value. Divide the numerator and denominator by the same common factor.

Example: Simplify 12/18

  1. Find a common factor of 12 and 18. Their greatest common factor is 6.
  2. Divide the numerator: 12 ÷ 6 = 2.
  3. Divide the denominator: 18 ÷ 6 = 3.
  4. The simplest form is 2/3.
Check: 2/3 × 6/6 = 12/18. The fractions are equivalent.

4. How to Check if Fractions Are Equivalent

You can simplify both fractions and see whether they become the same fraction.

Example: Are 3/4 and 6/8 equivalent?

  1. Start with 3/4.
  2. Multiply the numerator and denominator by 2: 3/4 = 6/8.
  3. The result matches the second fraction.

Answer: Yes, 3/4 and 6/8 are equivalent.

Another example: Are 2/3 and 3/5 equivalent?

2/3 cannot be changed into 3/5 by multiplying or dividing both terms by the same factor. Their values are different, so they are not equivalent.

5. Common Mistakes to Avoid

Changing only the numerator: Multiplying the top number but not the bottom number changes the fraction's value.
Changing only the denominator: Both parts must be multiplied or divided by the same non-zero number.
Stopping before simplest form: A fraction is fully simplified when the numerator and denominator have no common factor greater than 1.
Assuming bigger numbers mean a bigger fraction: 2/4 and 1/2 have different numbers but the same value.

6. Step-by-Step Practice Examples

Example 1: Find a fraction equivalent to 3/8 with denominator 24

8 × 3 = 24, so multiply the numerator by 3 as well: 3 × 3 = 9. Answer: 9/24.

Example 2: Simplify 15/20

The greatest common factor is 5. Divide both numbers by 5: 15 ÷ 5 = 3 and 20 ÷ 5 = 4. Answer: 3/4.

Example 3: Fill the missing number

4/5 = ?/20. Since 5 × 4 = 20, multiply the numerator by 4 too: 4 × 4 = 16. Answer: 16/20.

7. Practice Exercises

Try these questions before checking the answers.

  1. Write a fraction equivalent to 1/3 by multiplying both terms by 4.
  2. Write a fraction equivalent to 2/5 with denominator 20.
  3. Simplify 8/12.
  4. Simplify 18/24.
  5. Complete: 3/7 = 12/____.
  6. Are 4/6 and 2/3 equivalent? Explain briefly.
Show practice answers
  1. 4/12.
  2. 8/20.
  3. 2/3.
  4. 3/4.
  5. 28, because 7 is multiplied by 4 to get 28.
  6. Yes. Dividing 4/6 by 2/2 gives 2/3.

8. Test Your Understanding

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

1. Which fraction is equivalent to 1/2?
2. What is 2/3 with denominator 12?
3. What is 10/15 in simplest form?
4. Which action makes an equivalent fraction?
5. Complete: 3/4 = 15/?

9. Free Printable Worksheet

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

Learnora — Grade 6 Mathematics

Equivalent Fractions Worksheet

Name: __________________________ Date: _______________

Instructions: Answer all questions. Show your working where needed.

  1. Write a fraction equivalent to 2/3 by multiplying both terms by 5.
  2. Complete: 3/4 = 12/____.
  3. Simplify 6/10.
  4. Simplify 21/28.
  5. Are 5/8 and 10/16 equivalent? Explain.
  6. Write two fractions equivalent to 3/5.
  7. Explain the rule for making an equivalent fraction.

Great work! Keep practising.

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 10/15.
  2. 16.
  3. 3/5.
  4. 3/4.
  5. Yes. Multiply 5/8 by 2/2 to get 10/16.
  6. Examples: 6/10 and 9/15.
  7. Multiply or divide both numerator and denominator by the same non-zero number.

10. Lesson Summary

Next learning goal: Use equivalent fractions to compare and order fractions with different denominators.

Educational note: This is a curriculum-neutral introductory lesson. Teachers and parents can adapt the examples to their local curriculum.