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Equivalent Fractions

Class 6 Maths · Chapter 7: Fractions · NCERT Ganita Prakash section 7.6

Learn

Ira and Kabir each get the same-size cake. Ira cuts hers in 2 and eats 1 piece. Kabir cuts his in 4 and eats 2 pieces. They ate the same amount! So 1/2 = 2/4. Fractions that are equal are called equivalent fractions.

Look at the fraction wall. One 1/2 brick is as long as two 1/4 bricks, three 1/6 bricks and four 1/8 bricks. So 1/2 = 2/4 = 3/6 = 4/8.

The rule: multiply (or divide) the top and the bottom by the same number. 2/3 = (2 × 4)/(3 × 4) = 8/12. Cutting every piece into 4 smaller pieces does not change how much you have.

2/3 = 8/12

A fraction is in lowest terms when the top and bottom have no common factor except 1. To get there, divide both by their biggest common factor: 12/18 → ÷ 6 → 2/3.

12/18 = 6/9 = 2/3

Explore: make equivalent fractions. Change the number of parts and shade the same amount.

  1. Shade 1/2.
  2. Now show the same amount using 6 parts.
  3. Show 2/3 using 9 parts.
  4. Show 3/4 using 8 parts.

Remember

  • Equivalent fractions name the same amount: 1/2 = 2/4 = 3/6.
  • Multiply or divide the top and bottom by the same number. Adding the same number does not work.

Quick check

Which fraction is NOT equal to 2/5?

  1. 3/6
  2. 4/10
  3. 6/15
  4. 20/50
Answer

3/6. 4/10, 6/15 and 20/50 come from multiplying 2 and 5 by the same number. 3/6 = 1/2, which is not 2/5.

Think about it

Zoya says 2/3 = 3/4 because she added 1 to the top and the bottom. Use a picture to check her idea.

One answer

Draw two equal strips: 2/3 is 8/12 and 3/4 is 9/12. They are not equal (3/4 is a little more), so adding the same number to the top and bottom changes the fraction.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.