Class 7 Mathematics

Chapter 8 Solutions — Working with Fractions

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Solutions

Overview

Step-by-step NCERT solutions for Working with Fractions (Chapter 8, NCERT Class 7 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Working with Fractions textbook chapter.

Solved

What these solutions cover

All 24 questions in Working with Fractions are solved in the PDF. Here's what's inside, exercise by exercise:

Figure it Out

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?
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.
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?
Safia saw the Moon setting on Monday at 10 pm. Her mother, who is a scientist, told her that 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?
5.
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

Figure it Out — Unit Fraction Products

1.
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. Now, find 1/12 × 1/18.
2.
Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations:
- (a) 2/3 × 4/5
- (b) 1/4 × 2/3
- (c) 3/5 × 1/2
- (d) 4/6 × 3/5

Figure it Out — Fraction Multiplication Problems

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 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?
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…
Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.
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.
Which is heavier: 12/15 of 500 grams or 3/20 of 4 kg?

Figure it Out — Division of Fractions

1.
Evaluate the following:
- (a) 3 ÷ 7/9
- (b) 14/4 ÷ 2
- (c) 2/3 ÷ 2/3
- (d) 14/6 ÷ 7/3
- (e) 4/3 ÷ 3/4
- (f) 7/4 ÷ 1/7
- (g) 8/2 ÷ 4/15
- (h) 1/5 ÷ 1/9
- (i) 1/6 ÷ 11/12
- (j) 3 2/3 ÷ 1 3/8
2.
For each of the questions below, choose the expression that describes the solution. Then 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? Options:
- (i) 8 × 1/4
- (ii) 1/8 × 1/4
- (iii) 8 ÷ 1/4
- (iv) 1/4 ÷ 8.
- (b) 1/2 meter of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge? Options:
- (i) 8…
If 1/4 kg of flour is used to make 12 rotis, how much flour is used 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 1 ÷ 1/6, 1 ÷ 1/10, 1 ÷ 1/13, 1 ÷ 1/9, and 1 ÷ 1/2?' What should the friend say?
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?
A car runs 16 km using 1 litre of petrol. How far will it go using 2 3/4 litres of petrol?
Amritpal decides on a destination for his vacation. 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?
Mariam's grandmother baked 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?
9.
Choose the option(s) describing the product of (565/465 × 707/676):
- (a) > 565/465
- (b) < 565/465
- (c) > 707/676
- (d) < 707/676
- (e) > 1
- (f) < 1
What fraction of the whole square is shaded? [The square is divided into 4 equal quadrants. In the bottom-right quadrant, a diagonal splits it into two half-quadrant triangles; the shaded hatched triangle occupies 3/4 of the lower half-quadrant triangle.]
A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in Fig. 8.7) 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?
12.
Evaluate:
- (a) 1 − 1/2
- (b) (1 − 1/2) × (1 − 1/3)
- (c) (1 − 1/2) × (1 − 1/3) × (1 − 1/4) × (1 − 1/5)
- (d) (1 − 1/2) × (1 − 1/3) × (1 − 1/4) × (1 − 1/5) × (1 − 1/6) × (1 − 1/7) × (1 − 1/8) × (1 − 1/9) × (1 − 1/10). Make a general statement and explain.

Sample

Worked examples

3 questions from Working with Fractions, solved step by step.

Figure it Out

Safia saw the Moon setting on Monday at 10 pm. Her mother, who is a scientist, told her that 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?

Thursday is 3 days after Monday.

Total extra hours = 3 × 5/6 = 15/6 = 5/2 = 2 1/2 hours.

So the Moon sets 2 1/2 hours after 10 pm, i.e., at 12:30 am.

Answer: 2 1/2 hours after 10 pm (at 12:30 am).

Figure it Out — Fraction Multiplication Problems

Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.

Convert to improper fractions:

3 3/4 = 15/4 ft.

9 3/5 = 48/5 ft.

Area = 15/4 × 48/5.

Cancel common factors: 15 and 5 share factor 5 → 3/4 × 48/1.

Cancel 48 and 4: 3 × 12 = 36.

Area = 36 sq ft.

Answer: 36 sq ft

Figure it Out — Division of Fractions

If 1/4 kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?

Flour per roti = 1/4 ÷ 12 = 1/4 × 1/12 = 1/48 kg.

Flour for 6 rotis = 6 × 1/48 = 6/48 = 1/8 kg.

Alternatively: 6 rotis is half of 12 rotis, so flour = 1/2 × 1/4 = 1/8 kg.

Answer: 1/8 kg

All 24 questions in Working with Fractions are solved step by step in the Solutions PDF above.

Keep solving

Chapter 8 Solutions — Working with Fractions

Overview

What these solutions cover

Figure it Out

Figure it Out — Unit Fraction Products

Figure it Out — Fraction Multiplication Problems

Figure it Out — Division of Fractions

Worked examples

Safia saw the Moon setting on Monday at 10 pm. Her mother, who is a scientist, told her that 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?

Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.

If 1/4 kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?

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