EN हिं

NCERT Solutions Ganita Prakash Chapter 7 Brahmagupta’s method for subtracting fractions — Figure it Out

Book page 182 Updated on2026-09-05

Q1.
Carry out the following subtractions using Brahmagupta’s method: a. 8⁄15 – 3⁄15 b. 2⁄5 – 4⁄15 c. 5⁄6 – 4⁄9 d. 2⁄3 – 1⁄2
Answer
a. Same fractional unit already:
8/15 − 3/15 = 5/15 = (5 ÷ 5)/(15 ÷ 5) = 1/3
b. 15 is a multiple of 5, so change only the first fraction:
2/5 = (2 × 3)/(5 × 3) = 6/15
6/15 − 4/15 = 2/15
c. The smallest common multiple of 6 and 9 is 18:
5/6 = 15/18,   4/9 = 8/18
15/18 − 8/18 = 7/18
d. Common denominator 6:
2/3 = 4/6,   1/2 = 3/6
4/6 − 3/6 = 1/6
Q2.
Subtract as indicated: a. 13⁄4 from 10⁄3 b. 18⁄5 from 23⁄3 c. 29⁄7 from 45⁄7
Answer

“A from B” means B − A.

a. 10/3 − 13/4, common denominator 12:
10/3 = 40/12,   13/4 = 39/12
40/12 − 39/12 = 1/12
b. 23/3 − 18/5, common denominator 15:
23/3 = 115/15,   18/5 = 54/15
115/15 − 54/15 = 61/15 = 4 1/15
c. 45/7 − 29/7, same fractional unit:
(45 − 29)/7 = 16/7 = 2 2/7
Q3.
Solve the following problems: a. Jaya’s school is 7⁄10 km from her home. She takes an auto for 1⁄2 km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school? b. Jeevika takes 10⁄3 minutes to take a complete round of the park and her friend Namit takes 13⁄4 minutes to do the same. Who takes less time and by how much?
Answer

(a) Walking distance = total distance − auto distance.

7/10 − 1/2
1/2 = 5/10
7/10 − 5/10 = 2/10 = 1/5 km

Jaya walks 1⁄5 km (200 m) every day.

(b) Compare 10⁄3 and 13⁄4 using the common denominator 12.

Jeevika: 10/3 = 40/12 minutes
Namit: 13/4 = 39/12 minutes
39/12 < 40/12, so Namit is faster
Difference = 40/12 − 39/12 = 1/12 minute

Namit takes less time — by 1⁄12 of a minute (5 seconds).

Was this helpful? Report an error