Hinglish

Adding and Subtracting Fractions

Class 6 Maths · Chapter 7: Fractions · NCERT Ganita Prakash section 7.8, 7.9

Learn

Divit paints 2/7 of a fence in the morning and 3/7 in the evening. Both are pieces of size 1/7, so just count: 2 + 3 = 5 pieces. He painted 5/7.

2/7 + 3/7 = 5/7

Same bottom: add (or subtract) the tops and keep the bottom. 7/9 − 4/9 = 3/9 (= 1/3). The bottom stays the same because the size of each piece does not change.

7/9 − 4/9 = 3/9

Different bottoms: 1/2 + 1/3. Halves and thirds are different sizes, so first change both to sixths: 1/2 = 3/6 and 1/3 = 2/6. Now 3/6 + 2/6 = 5/6.

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Nisha has 3/4 of a bottle of juice and pours out 1/3 of the bottle. Use 12ths: 9/12 − 4/12 = 5/12 of the bottle is left.

3/4 − 1/3 = 9/12 − 4/12 = 5/12

Explore: add by jumping on the number line.

  1. Start at 0. Jump 3/8, then 2/8 more. Where do you land?
  2. 1/2 + 1/4: change both to eighths and land on the answer.
  3. Start at 7/8 and jump back 3/8.

From history: Indian mathematicians wrote fractions with one number above the other, without a line between them. Around 1,400 years ago, Brahmagupta wrote clear rules for adding and subtracting fractions with different bottoms: change them so the bottoms match, then add the tops. The line between the numbers was added later, by mathematicians in North Africa.

Remember

  • Same bottom: add or subtract the tops, keep the bottom.
  • Different bottoms: first rewrite with a common bottom, then add or subtract.
  • Never add the bottoms: 1/2 + 1/2 is 1, not 2/4.

Quick check

2/5 + 1/2 = ?

  1. 9/10
  2. 3/7
  3. 3/10
  4. 1/10
Answer

9/10. Use tenths: 2/5 = 4/10 and 1/2 = 5/10, so 4/10 + 5/10 = 9/10. Adding tops and bottoms (3/7) is a common mistake.

Think about it

Rohan reads 1/3 of a book on Monday and 1/4 on Tuesday. What fraction of the book is still unread?

One answer

Use 12ths: 1/3 = 4/12 and 1/4 = 3/12, so he has read 7/12. The whole book is 12/12, so 12/12 − 7/12 = 5/12 is still unread.

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.