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Mixed Fractions

Class 6 Maths · Chapter 7: Fractions · NCERT Ganita Prakash section 7.5

Learn

Anjali shares 7 rotis between 2 plates equally. Each plate gets 3 whole rotis, and the last roti is cut in half. Each plate has 3 and a half rotis, written 3 1/2.

7 ÷ 2 = 3 and 1 left → 3 1/2

A fraction whose top is bigger than its bottom, like 7/2, is more than one whole. Written as whole + a fraction smaller than 1, it becomes a mixed fraction: 7/2 = 3 1/2.

Fraction → mixed: 11/4. How many whole 4s are in 11? Two (8), with 3 left over. So 11/4 = 2 3/4.

11 = 2 × 4 + 3 → 2 3/4

Mixed → fraction: 2 1/3. Each whole is 3 thirds, so 2 wholes are 6 thirds; add 1 more third: 7/3.

2 × 3 + 1 = 7 → 7/3

Explore: shade across three strips to make fractions bigger than 1.

  1. Shade 5/4. How many whole strips is that?
  2. Shade 2 3/4.
  3. These strips are cut in thirds. Shade 1 2/3.

Remember

  • A fraction more than 1 can be written as a mixed fraction: 11/4 = 2 3/4.
  • Mixed → fraction: whole × bottom + top, over the same bottom: 2 3/4 = 11/4.

Quick check

Which mixed fraction equals 9/4?

  1. 2 1/4
  2. 1 4/9
  3. 2 4/1
  4. 4 1/2
Answer

2 1/4. 9 = 2 × 4 + 1, so 9/4 = 2 whole and 1/4.

Think about it

Tenzin says 13/5 is bigger than 3. Is he right?

One answer

No. 3 = 15/5, and 13/5 is less than 15/5. In fact 13/5 = 2 3/5, which lies between 2 and 3.

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.