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08
NCERT Solutions · Maths Ch 8
Working with Fractions
26 questions · 4 exercises
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Ex 8.1
Ex 8.2
Ex 8.3
Ex 8.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 8.1 · 5 QUESTIONS
Multiplication by Whole Numbers
Q1
Tenzin drinks 1/2 glass of milk every day. How many glasses of milk does he drink in a week? How many glasses of milk did he drink in the month of January?
(2 marks)
Q2
A team of workers can make 1 km of a water canal in 8 days. So in one day the team can make ___ km. If they work 5 days a week, they can make ___ km in a week.
(2 marks)
Q3
Manju and two of her neighbours buy 5 litres of oil every week and share it equally among the 3 families. How much oil does each family get in a week? How much oil will one family get in 4 weeks?
(2 marks)
Q4
Safia saw the Moon setting on Monday at 10 pm. Every day the Moon sets 5/6 hour later than the previous day. How many hours after 10 pm will the moon set on Thursday?
(2 marks)
Q5
Multiply and then convert it into a mixed fraction: (a) 7 × 3/5 (b) 4 × 1/3 (c) 9/7 × 6 (d) 13/11 × 6
(3 marks)
2
EXERCISE 8.2 · 7 QUESTIONS
Multiplication of Fractions
Q6
Find the following products. Use a unit square as a whole for representing the fractions: (a) 1/3 × 1/5 (b) 1/4 × 1/3 (c) 1/5 × 1/2 (d) 1/6 × 1/5
(2 marks)
Q7
Find the following products. Use a unit square as a whole for representing the fractions: (a) 2/3 × 4/5 (b) 1/4 × 2/3 (c) 3/5 × 1/2 (d) 4/6 × 3/5
(3 marks)
Q8
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 hour (b) 2/3 hour (c) 3/4 hour (d) 7/10 hour (e) For the tank to be full, how long should the tap be running?
(3 marks)
Q9
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 to her daughter Krishna and 1/3 of it to her son Bora. She keeps the remaining land. (a) What part of the original land did Krishna get? (b) What part did Bora get? (c) What part did Somu keep for herself?
(3 marks)
Q10
Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.
(2 marks)
Q11
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 sapling.
(2 marks)
Q12
Which is heavier: 12/15 of 500 grams or 3/20 of 4 kg?
(3 marks)
3
EXERCISE 8.3 · 2 QUESTIONS
Division of Fractions
Q13
Four fountains fill a cistern. The first fountain can fill the cistern in a day, the second in 1/2 day, the third in 1/4 day and the fourth in 1/5 day. In a day, how many times will each fountain fill the cistern, and how many times will the four fountains together fill it?
(3 marks)
Q14
In each of the figures given, find the fraction of the big square that the shaded region occupies. (a) a square divided into parts with some shaded (b) a square with a small shaded region
(2 marks)
4
12 QUESTIONS
Exercise 8.4
Q15
Evaluate the following: 3 ÷ 7/9; 14/4 ÷ 2; 2/3 ÷ 2/3; 14/6 ÷ 7/3; 4/3 ÷ 3/4; 7/4 ÷ 1/7; 8/2 ÷ 4/15; 1/5 ÷ 1/9; 1/6 ÷ 11/12; 3 2/3 ÷ 1 3/8
(5 marks)
Q16
Choose the expression that describes the solution and simplify it. (a) Maria bought 8 m of lace; she used 1/4 m for each bag and finished the lace. How many bags did she decorate? (b) 1/2 metre of ribbon is used to make 8 badges. What is the length of ribbon used for each badge? (c) A baker needs 1/6 kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves can he make?
(3 marks)
Q17
If 1/4 kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?
(2 marks)
Q18
Patiganita (Sridharacharya, 9th century) asks: 'Friend, what sum will be obtained by adding together 1 ÷ 1/6, 1 ÷ 1/10, 1 ÷ 1/13, 1 ÷ 1/9 and 1 ÷ 1/2?'
(3 marks)
Q19
Mira is reading a novel that has 400 pages. She read 1/5 of the pages yesterday and 3/10 of the pages today. How many more pages does she need to read to finish the novel?
(2 marks)
Q20
A car runs 16 km using 1 litre of petrol. How far will it go using 2 3/4 litres of petrol?
(2 marks)
Q21
Amritpal decides on a destination. If he takes a train, it will take him 5 1/6 hours to get there. If he takes a plane, it will take him 1/2 hour. How many hours does the plane save?
(2 marks)
Q22
Mariam's grandmother made a cake. Mariam and her cousins finished 4/5 of the cake. The remaining cake was shared equally by Mariam's three friends. How much of the cake did each friend get?
(2 marks)
Q23
Choose the option(s) describing the product of 565/465 × 707/676: (a) > 565/465 (b) 707/676 (d) 1 (f) (3 marks)
Q24
What fraction of the whole square is shaded? (the figure on page 197)
(1 mark)
Q25
A colony of ants set out in search of food. As they search, they keep splitting equally at each point and reach two food sources, one near a mango tree and another near a sugarcane field (Fig. 8.7). What fraction of the original group reached each food source?
(2 marks)
Q26
What is 1 − 1/2? Evaluate (1 − 1/2) × (1 − 1/3); (1 − 1/2) × (1 − 1/3) × (1 − 1/4) × (1 − 1/5); and (1 − 1/2) × (1 − 1/3) × … × (1 − 1/10). Make a general statement and explain.
(3 marks)