Hinglish

Comparing Fractions

Class 6 Maths · Chapter 7: Fractions · NCERT Ganita Prakash section 7.7

Learn

Same bottom: 3/7 and 5/7 both count pieces of size 1/7. Five pieces are more than three, so 5/7 > 3/7.

Same top: 3/5 and 3/8 both have 3 pieces, but fifths are bigger than eighths. So 3/5 > 3/8.

Different tops and bottoms: compare 2/3 and 3/4. Write both with the same bottom, a common multiple of 3 and 4: 2/3 = 8/12 and 3/4 = 9/12. Now 9 > 8, so 3/4 > 2/3.

8/12 < 9/12

Sahil runs 5/6 of a lap and Gauri runs 7/9 of the same lap. Who ran further? Use 18ths: 5/6 = 15/18 and 7/9 = 14/18. Sahil ran further, by 1/18 of a lap.

15/18 > 14/18

Explore: compare on the number line. Place each fraction and see which is further right.

  1. Put the point at 2/3.
  2. Now put it at 5/8. Is it left or right of where 2/3 was?
  3. Use 12 gaps and place the bigger of 2/3 and 3/4.

Remember

  • Same bottom: bigger top is bigger. Same top: smaller bottom is bigger.
  • Otherwise, make the bottoms the same using a common multiple, then compare the tops.

Quick check

Which is the biggest?

  1. 5/6
  2. 2/3
  3. 3/4
  4. 1/2
Answer

5/6. In 12ths: 5/6 = 10/12, 2/3 = 8/12, 3/4 = 9/12, 1/2 = 6/12. The biggest is 10/12 = 5/6.

Think about it

Find a fraction that lies between 1/3 and 1/2.

One answer

Use 12ths: 1/3 = 4/12 and 1/2 = 6/12. 5/12 is between them. (Using 24ths gives even more, like 9/24 and 10/24.)

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.