NCERT Solutions for Class 7 maths Chapter 8: Working with Fractions

Tenzin drinks 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?
Solution:
Number of glasses of milk drink in a day =
There are 7 days in a week.
So, number of glasses of milk drink in 1 week = 7 × = = 3
Therefore, Tenzin drinks 3 glasses of milk in a week.
Also, there are 31 days in the month of January.
So, number of glasses of milk drink in the month of January = 31 × = = 15
Therefore, Tenzin drinks 15 glasses of milk in the month of January.

A team of workers can make 1 km of a water canal in 8 days. So, in one day, the team can make __________ km of the water canal. If they work 5 days a week, they can make __________ km of the water canal in a week.
Solution:
Water canal made by team of workers in 8 days = 1 km
So, water canal made by team of workers in 1 day = km
The length of the water canal made by the team of workers in 5 days = 5 × km = km
Hence, the team can make km of the water canal in one week.

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?
Solution:
The amount of oil each family gets in a week = litres
The amount of oil one family gets in 4 week = 4 × litres = litres = 6 litres

Safia saw the Moon setting on Monday at 10 pm. Her mother, who is a scientist, told her that every day the Moon sets hours later than the previous day. How many hours after 10 pm will the moon set on Thursday?
Solution:
There are 3 days from Monday to Thursday.
Since the Moon sets hours later than previous day,
the number of hours the Moon will set later on Thursday than Monday = 3 × hours
= hours
= hours
We know that 1 hour = 60 minutes
hours = × 60 minutes = minutes = 150 minutes
Now, 150 minutes =120 minutes + 30 minutes = 2 hours 30 minutes
Hence, on Thursday the Moon will set 2 hours 30 minutes after 10 pm.

Multiply and then convert it into a mixed fraction:
(a) 7 ×
(b) 4 ×
(c) × 6
(d) × 6
Solution:

Find the following products. Use a unit square as a whole for representing the fractions:
(a)
(b)
(c)
(d)
Solution:
(a) Each row represents and each column represents .
The whole is divided into 5 rows and 3 columns, creating 5 × 3 = 15 equal parts and one of the parts
is double-shaded, that is of the whole is double-shaded.
Therefore,

Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations.
(a)
(b)
(c)
(d)
Solution:
(a) Each row represents and each column represents .
The whole is divided into 5 rows and 3 columns creating 5 × 3 = 15 equal parts and 2 × 4 = 8 of the parts are double-shaded, that is of the whole is double-shaded.
Therefore,

A water tank is filled from a tap. If the tap is open for 1 hour, of the tank gets filled. How much of the tank is filled if the tap is open for
(a) hour ___________
(c) hour ___________
(b) hour ___________
(d) hour ___________
(e) For the tank to be full, how long should the tap be running?
Solution:
In 1 hour, part of the tank gets filled =
(a) In hour, part of the tank gets filled = =
Therefore, in hours, of the tank gets filled.

The government has taken 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 it to her son Bora. After giving them their shares, she kept 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?
Solution:
After part of the land acquiring by government,
The land remaining with Somu is 1 – = parts
(a) Krishna got half of the remaining land.
Since the remaining land is of the original land.
So, Krishna get of the original land = =
Thus, Krishna got of the original land.

Find the area of a rectangle of sides 3 ft and 9 ft.
Solution:

Tsewang plants four saplings in a row in his garden. The distance between two saplings is m. Find the distance between the first and last sapling.
[Hint: Draw a rough diagram with four saplings with distance between two saplings as m]
Solution:

Which is heavier: of 500 grams or of 4 kg?
Solution:

Evaluate the following:

Solution:

For each of the questions below, choose the expression that describes the solution. Then simplify it.
(a) Maria bought 8 m of lace to decorate the bags she made for school. She used m for each bag and finished the lace. How many bags did she decorate?
(i) 8 ×
(ii)
(iii) 8 ÷
(iv) ÷ 8
(b) metre of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i) 8 ×
(ii)
(iii) 8 ÷
(iv) ÷ 8
(c) A baker needs kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make?
(i) 5 ×
(ii) ÷ 5
(iii) 5 ÷
(iv) 5 × 6
Solution:
(a) To find the total number of bags Maria decorates, we need to divide the total length of lace by the length of the lace required to decorate one bag, i.e., 8 ÷ .
Hence, the correct expression that describes the solution is (iii) 8 ÷
Now, 8 ÷ = 8 × 4 = 32

If of flour is used to make 12 rotis, how much flour is used to make 6 rotis?
Solution:
If kg of flour is required to make 12 rotis, then the amount of flour required to make 6 rotis will be half of kg,
i.e.,
Hence, kg of flour is required to make 6 rotis.

Patiganita, a book written by Sridharacharya in the 9th century CE, mentions this problem: “Friend, after thinking, what sum will be obtained by adding together , and 1 ÷ ”. What should the friend say?
Solution:

Mira is reading a novel that has 400 pages. She read of the pages yesterday and of the pages today. How many more pages does she need to read to finish the novel?
Solution:
of 400 = × 400 = = 80
of 400 = × 400 = 120
∴ Total number of pages read by Mira = 120 + 80 = 200
Thus, the number of papers she needs to read to finish the novel = 400 – 200 = 200.

A car runs 16 km using 1 litre of petrol. How far will it go using 2 litres of petrol?
Solution:
∴ In 1 litre of petrol, the car runs 16 km.
∴ In 2 litres of petrol, the car will run

Amritpal decides on a destination for his vacation. If he takes a train, it will take him 5 hours to get there. If he takes a plane, it will take him hour. How many hours does the plane save?
Solution:
The difference between the two durations

Hence, the plane saves 4 hours.

Mariam’s grandmother baked a cake. Mariam and her cousins finished of the cake. The remaining cake was shared equally by Mariam’s three friends. How much of the cake did each friend get?
Solution:
The remaining cake is
So, of the cake is shared equally by Mariam’s three friends.
∴ Each of the friend got
∴ Thus, each friend got of the cake.

Choose the option(s) describing the product of :
(a) >
(b) < (c) >
(d) < (e) > 1
(f) < 1
Solution:

Hence, the correct options are (a), (c), and (e).

What fraction of the whole square is shaded?

Solution:
In the given figure, the big square is divided into 4 identical squares.
So, one small square occupies of the area of the big square.
Now, consider the smaller square

The square in the above figure is divided into 8 identical triangles, of which 3 are the shaded parts.
So, the shaded part is of the small square.
But the small square is of the big square.
The shaded part is of the big square.
Hence, of the whole square is shaded.

A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in the figure) and reach two food sources, one near a mango tree and another near a sugarcane field. What fraction of the original group reached each food source?

Solution:
At first point ants split into two ways.
So, fraction of ants at each way is 1 ÷ 2 =

At the second point, ants split into two ways.
So fraction of ants at each way =
At the third point, ants split into four ways.
So, fraction of ants at each way =
At the fourth point, ants split into 2 ways.
So fraction of ants at each way =
Hence, a fraction of ants at the mango tree is

Fraction of ants near sugarcane field is

What is 1 – ?

Make a general statement and explain.
Solution:

Here, we observe that in this pattern of product denominator of each term cancels the numerator of the next term, and the final product is the numerator of the first term and the denominator of the last term.
In general,