Exercise 8.3 of Chapter 8 covers the topic of dividing fractions, a vital concept in mathematics. In this exercise, you will learn about dividing a whole number by a fraction, a fraction by a whole number, and a fraction by a fraction. All of these questions are not only assessed practically in exams, but also in reality, where they relate to practical examples.
The questions in this exercise are based on the NCERT syllabus Class 7 Maths, and practicing this exercise will help you understand how to do division problems with fractions in a simple manner, while also improving your speed and accuracy in exam situations.
Along with the exercise we have also provided detailed NCERT Solutions for all of the questions in the exercise. Each step in the solutions is explained thoroughly so you can better understand the concept of division with fraction problems and avoid mistakes.
Exercise 8.3 describes dividing fractions and whole numbers. The NCERT Solutions of Class 7 Maths Chapter 8 give easy to follow steps for each question. Download the free PDF of the solutions from below:
Exercise 8.3 mainly focuses on division involving fractions. It builds on the earlier topics. Here are the key concepts included:
1. A water tank is filled from a tap. If the tap is open for 1 hour, 7/10 of the tank gets filled. How much of the tank is filled if the tap is open for:
(a) 1/3 hours
(b) 2/3 hours
(c) 3/4 hours
(d) 7/10 hours
(e) For the tank to be full, how long should the tap be running?
Sol. Rate of filling = 7/10 of the tank per hour.
(a) Time = 1/3 hour. Fraction filled = 7/10 x 1/3 = 7/30
(b) Time = 2/3 hours. Fraction filled = 7/10 x 2/3 = 14/30 = 7/15
(c) Time = 3/4 hours. Fraction filled = 7/10 x 3/4 = 21/40
(d) Time = 7/10 hours. Fraction filled = 7/10 x 7/10 = 49/100
(e) For the tank to be full (1 whole tank).
(7/10) x x = 1
x = 1 / (7/10)
x = 10/7 hours.
Answer: The tap should be running for 10/7 hours to fill the tank completely.
2. The government has taken 1/6 of Somu's land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and 1/3 of it to her son Bora. After giving them their shares, she keeps the remaining land for herself.
(a) What part of the original land did Krishna get?
(b) What part of the original land did Bora get?
(c) What part of the original land did Somu keep for herself?
Sol.
Total land remaining with Somu after road construction = 1 - 1/6 = 5/6.
(a) Krishna's share (half of remaining) = 1/2 x 5/6 = 5/12 of the original land.
(b) Bora's share (1/3 of remaining) = 1/3 x 5/6 = 5/18 of the original land.
(c) Somu's share = Remaining land - (Krishna's share + Bora's share)
= 5/6 - (5/12 + 5/18)
To add Krishna's and Bora's shares, use LCM(12, 18) = 36:
5/12 + 5/18 = (5x3)/36 + (5x2)/36 = 15/36 + 10/36 = 25/36.
Somu's share = 5/6 - 25/36
To subtract, convert 5/6 to 36ths: (5x6)/(6x6) = 30/36.
Somu's share = 30/36 - 25/36 = 5/36.
3. Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.
Sol.
Sides of the rectangle: 3 3/4 ft and 9 3/5 ft.
Convert to improper fractions:
3 3/4 = (3x4 + 3)/4 = 15/4 ft
9 3/5 = (9x5 + 3)/5 = 48/5 ft
Area of rectangle = length x breadth
Area = 15/4 x 48/5
Area = (15 x 48) / (4 x 5)
Area = (15/5) x (48/4)
Area = 3 x 12 = 36.
The area of the rectangle is 36 square feet.
4. Tsewang plants four saplings in a row in his garden. The distance between two saplings is 3/4 m. Find the distance between the first and last saplings.
Sol.
Number of saplings = 4.
and distance between two saplings = 3/4 m
Number of gaps between saplings = 4 - 1 = 3
Total distance between the first and last saplings = 3 x 3/4
= 9/4 m
Convert to a mixed number: 9/4 = 2 1/4 m
So, the distance between the first and last saplings is 2 1/4 metres.
5. Which is heavier: 12/15 of 500 grams or 3/20 of 4 kg?
Sol.
Calculate the weight for the first quantity:
12/15 of 500 grams = 12/15 x 500 grams
= 6000 / 15 grams
= 400 grams
Calculate the weight for the second quantity (convert 4 kg to 4000 grams):
3/20 of 4 kg = 3/20 x 4000 grams
= 12000 / 20 grams
= 600 grams
Since 600 grams is heavier than 400 grams,
3/20 of 4 kg is heavier.
(Session 2026 - 27)