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NCERT Solutions

Working with Fractions

CBSE · Class 7 · Mathematics

NCERT Solutions for Working with Fractions — CBSE Class 7 Mathematics.

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Figure it Out — Multiplying a Fraction and a Whole Number

1Tenzin drinks 12\frac{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?Show solution
Given: Tenzin drinks 12\frac{1}{2} glass of milk every day.

In a week (7 days):
7×12=72=312 glasses7 \times \frac{1}{2} = \frac{7}{2} = 3\frac{1}{2} \text{ glasses}

In January (31 days):
31×12=312=1512 glasses31 \times \frac{1}{2} = \frac{31}{2} = 15\frac{1}{2} \text{ glasses}

Answer: Tenzin drinks 3123\frac{1}{2} glasses in a week and 151215\frac{1}{2} glasses in January.

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2A 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.Show solution
Given: The team makes 1 km in 8 days.

In one day:
18 km\frac{1}{8} \text{ km}

In 5 days (one week):
5×18=58 km5 \times \frac{1}{8} = \frac{5}{8} \text{ km}

Answer: In one day the team can make 18\frac{1}{8} km; in a week (5 working days) they can make 58\frac{5}{8} km of the water canal.

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3Manju 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?Show solution
Given: 5 litres shared equally among 3 families.

Oil per family per week:
53=123 litres\frac{5}{3} = 1\frac{2}{3} \text{ litres}

Oil per family in 4 weeks:
4×53=203=623 litres4 \times \frac{5}{3} = \frac{20}{3} = 6\frac{2}{3} \text{ litres}

Answer: Each family gets 1231\frac{2}{3} litres per week and 6236\frac{2}{3} litres in 4 weeks.

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4Safia saw the Moon setting on Monday at 10 pm. Her mother told her that every day the Moon sets 56\frac{5}{6} hour later than the previous day. How many hours after 10 pm will the moon set on Thursday?Show solution
Given: Moon sets 56\frac{5}{6} hour later each day. Monday is the starting day.

Number of days from Monday to Thursday: 3 days.

Total extra hours by Thursday:
3×56=156=52=212 hours3 \times \frac{5}{6} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2} \text{ hours}

Answer: The Moon will set 2122\frac{1}{2} hours after 10 pm on Thursday, i.e., at 12:30 am.

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5Multiply and then convert it into a mixed fraction:
(a) 7×357 \times \frac{3}{5}
(b) 4×134 \times \frac{1}{3}
(c) 97×6\frac{9}{7} \times 6
(d) 1311×6\frac{13}{11} \times 6Show solution
Formula used: Multiply the whole number with the numerator; keep the denominator the same. Then convert the improper fraction to a mixed fraction.

(a) 7×35=7×35=215=4157 \times \frac{3}{5} = \frac{7 \times 3}{5} = \frac{21}{5} = 4\frac{1}{5}

(b) 4×13=4×13=43=1134 \times \frac{1}{3} = \frac{4 \times 1}{3} = \frac{4}{3} = 1\frac{1}{3}

(c) 97×6=9×67=547=757\frac{9}{7} \times 6 = \frac{9 \times 6}{7} = \frac{54}{7} = 7\frac{5}{7}

(d) 1311×6=13×611=7811=7111\frac{13}{11} \times 6 = \frac{13 \times 6}{11} = \frac{78}{11} = 7\frac{1}{11}

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Figure it Out — Multiplying Two Fractions (Unit Fractions)

1Find the following products. Use a unit square as a whole for representing the fractions:
(a) 13×15\frac{1}{3} \times \frac{1}{5}
(b) 14×13\frac{1}{4} \times \frac{1}{3}
(c) 15×12\frac{1}{5} \times \frac{1}{2}
(d) 16×15\frac{1}{6} \times \frac{1}{5}

Now, find 112×118\frac{1}{12} \times \frac{1}{18}.Show solution
Formula used: 1b×1d=1b×d\frac{1}{b} \times \frac{1}{d} = \frac{1}{b \times d}

When a unit square is divided into bb rows and dd columns, it creates b×db \times d equal parts, and one such part represents the product.

(a) 13×15=13×5=115\frac{1}{3} \times \frac{1}{5} = \frac{1}{3 \times 5} = \frac{1}{15}

(b) 14×13=14×3=112\frac{1}{4} \times \frac{1}{3} = \frac{1}{4 \times 3} = \frac{1}{12}

(c) 15×12=15×2=110\frac{1}{5} \times \frac{1}{2} = \frac{1}{5 \times 2} = \frac{1}{10}

(d) 16×15=16×5=130\frac{1}{6} \times \frac{1}{5} = \frac{1}{6 \times 5} = \frac{1}{30}

Now: 112×118=112×18=1216\frac{1}{12} \times \frac{1}{18} = \frac{1}{12 \times 18} = \frac{1}{216}

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2Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations.
(a) 23×45\frac{2}{3} \times \frac{4}{5}
(b) 14×23\frac{1}{4} \times \frac{2}{3}
(c) 35×12\frac{3}{5} \times \frac{1}{2}
(d) 46×35\frac{4}{6} \times \frac{3}{5}Show solution
Formula used (Brahmagupta's rule): ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

The unit square is divided into rows equal to one denominator and columns equal to the other. The shaded region (numerator rows × numerator columns) gives the product.

(a) 23×45=2×43×5=815\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}

(b) 14×23=1×24×3=212=16\frac{1}{4} \times \frac{2}{3} = \frac{1 \times 2}{4 \times 3} = \frac{2}{12} = \frac{1}{6}

(c) 35×12=3×15×2=310\frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10}

(d) 46×35=4×36×5=1230=25\frac{4}{6} \times \frac{3}{5} = \frac{4 \times 3}{6 \times 5} = \frac{12}{30} = \frac{2}{5}

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Figure it Out — Multiplying Fractions (Applications)

1A water tank is filled from a tap. If the tap is open for 1 hour, 710\frac{7}{10} of the tank gets filled. How much of the tank is filled if the tap is open for
(a) 13\frac{1}{3} hour
(b) 23\frac{2}{3} hour
(c) 34\frac{3}{4} hour
(d) 710\frac{7}{10} hour
(e) For the tank to be full, how long should the tap be running?Show solution
Given: In 1 hour, 710\frac{7}{10} of the tank is filled.

So in tt hours, the fraction filled =t×710= t \times \frac{7}{10}.

(a) 13×710=730\frac{1}{3} \times \frac{7}{10} = \frac{7}{30} of the tank.

(b) 23×710=1430=715\frac{2}{3} \times \frac{7}{10} = \frac{14}{30} = \frac{7}{15} of the tank.

(c) 34×710=2140\frac{3}{4} \times \frac{7}{10} = \frac{21}{40} of the tank.

(d) 710×710=49100\frac{7}{10} \times \frac{7}{10} = \frac{49}{100} of the tank.

(e) For the tank to be full, we need the fraction filled =1= 1.
t×710=1  ⟹  t=1÷710=107=137 hourst \times \frac{7}{10} = 1 \implies t = 1 \div \frac{7}{10} = \frac{10}{7} = 1\frac{3}{7} \text{ hours}

Answer: The tap should run for 1371\frac{3}{7} hours for the tank to be full.

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2The government has taken 16\frac{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 13\frac{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?Show solution
Step 1: Land taken by government =16= \frac{1}{6}.

Land remaining with Somu =1−16=56= 1 - \frac{1}{6} = \frac{5}{6}.

Step 2: Somu gives half of 56\frac{5}{6} to Krishna:
Krishna’s share=12×56=512\text{Krishna's share} = \frac{1}{2} \times \frac{5}{6} = \frac{5}{12}

Step 3: Somu gives 13\frac{1}{3} of 56\frac{5}{6} to Bora:
Bora’s share=13×56=518\text{Bora's share} = \frac{1}{3} \times \frac{5}{6} = \frac{5}{18}

Step 4: Land Somu keeps:
56−512−518\frac{5}{6} - \frac{5}{12} - \frac{5}{18}
LCM of 6, 12, 18 = 36.
=3036−1536−1036=536= \frac{30}{36} - \frac{15}{36} - \frac{10}{36} = \frac{5}{36}

(a) Krishna got 512\frac{5}{12} of the original land.

(b) Bora got 518\frac{5}{18} of the original land.

(c) Somu kept 536\frac{5}{36} of the original land for herself.

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3Find the area of a rectangle of sides 3343\frac{3}{4} ft and 9359\frac{3}{5} ft.Show solution
Given: Length =935= 9\frac{3}{5} ft =485= \frac{48}{5} ft; Breadth =334= 3\frac{3}{4} ft =154= \frac{15}{4} ft.

Formula: Area == Length ×\times Breadth.

Area=485×154\text{Area} = \frac{48}{5} \times \frac{15}{4}

Cancelling common factors: 484=12\frac{48}{4} = 12 and 155=3\frac{15}{5} = 3:

=12×3=36 sq ft= 12 \times 3 = 36 \text{ sq ft}

Answer: The area of the rectangle is 3636 sq ft.

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4Tsewang plants four saplings in a row in his garden. The distance between two saplings is 34\frac{3}{4} m. Find the distance between the first and last sapling.Show solution
Given: 4 saplings in a row; distance between consecutive saplings =34= \frac{3}{4} m.

Concept: With 4 saplings, there are 4−1=34 - 1 = 3 gaps between them.

Distance from first to last sapling:
3×34=94=214 m3 \times \frac{3}{4} = \frac{9}{4} = 2\frac{1}{4} \text{ m}

Answer: The distance between the first and last sapling is 2142\frac{1}{4} m.

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5Which is heavier: 1215\frac{12}{15} of 500 grams or 320\frac{3}{20} of 4 kg?Show solution
Calculating each quantity:

First quantity: 1215\frac{12}{15} of 500 g
=1215×500=12×50015=600015=400 g= \frac{12}{15} \times 500 = \frac{12 \times 500}{15} = \frac{6000}{15} = 400 \text{ g}

Second quantity: 320\frac{3}{20} of 4 kg =320= \frac{3}{20} of 4000 g
=320×4000=1200020=600 g= \frac{3}{20} \times 4000 = \frac{12000}{20} = 600 \text{ g}

Comparison: 600600 g >400> 400 g.

Answer: 320\frac{3}{20} of 4 kg (= 600 g) is heavier than 1215\frac{12}{15} of 500 g (= 400 g).

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Figure it Out — Division of Fractions

1Evaluate the following:
3÷793 \div \frac{7}{9}, 144÷2\frac{14}{4} \div 2, 23÷23\frac{2}{3} \div \frac{2}{3}, 146÷73\frac{14}{6} \div \frac{7}{3},
43÷34\frac{4}{3} \div \frac{3}{4}, 74÷17\frac{7}{4} \div \frac{1}{7}, 82÷415\frac{8}{2} \div \frac{4}{15},
15÷19\frac{1}{5} \div \frac{1}{9}, 16÷1112\frac{1}{6} \div \frac{11}{12}, 323÷1383\frac{2}{3} \div 1\frac{3}{8}
2For 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 14\frac{1}{4} m for each bag and finished the lace. How many bags did she decorate?
(i) 8×148 \times \frac{1}{4} (ii) 18×14\frac{1}{8} \times \frac{1}{4} (iii) 8÷148 \div \frac{1}{4} (iv) 14÷8\frac{1}{4} \div 8

(b) 12\frac{1}{2} meter of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i) 8×128 \times \frac{1}{2} (ii) 12÷18\frac{1}{2} \div \frac{1}{8} (iii) 8÷128 \div \frac{1}{2} (iv) 12÷8\frac{1}{2} \div 8

(c) A baker needs 16\frac{1}{6} kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make?
(i) 5×165 \times \frac{1}{6} (ii) 16÷5\frac{1}{6} \div 5 (iii) 5÷165 \div \frac{1}{6} (iv) 5×65 \times 6
3If 14\frac{1}{4} kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?
4Pātīganita, 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÷161 \div \frac{1}{6}, 1÷1101 \div \frac{1}{10}, 1÷1131 \div \frac{1}{13}, 1÷191 \div \frac{1}{9}, and 1÷121 \div \frac{1}{2}'. What should the friend say?
5Mira is reading a novel that has 400 pages. She read 15\frac{1}{5} of the pages yesterday and 310\frac{3}{10} of the pages today. How many more pages does she need to read to finish the novel?
6A car runs 16 km using 1 litre of petrol. How far will it go using 2342\frac{3}{4} litres of petrol?
7Amritpal decides on a destination for his vacation. If he takes a train, it will take him 5165\frac{1}{6} hours to get there. If he takes a plane, it will take him 12\frac{1}{2} hour. How many hours does the plane save?
8Mariam's grandmother baked a cake. Mariam and her cousins finished 45\frac{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?
9Choose the option(s) describing the product of (565465×707676)\left(\frac{565}{465} \times \frac{707}{676}\right):
(a) >565465> \frac{565}{465}
(b) <565465< \frac{565}{465}
(c) >707676> \frac{707}{676}
(d) <707676< \frac{707}{676}
(e) >1> 1
(f) <1< 1
10What fraction of the whole square is shaded? (Refer to Fig. in textbook)
11A 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?
12What is 1−121 - \frac{1}{2}?

(1−12)×(1−13)\left(1 - \frac{1}{2}\right) \times \left(1 - \frac{1}{3}\right)?

(1−12)×(1−13)×(1−14)×(1−15)\left(1 - \frac{1}{2}\right) \times \left(1 - \frac{1}{3}\right) \times \left(1 - \frac{1}{4}\right) \times \left(1 - \frac{1}{5}\right)?

(1−12)×(1−13)×(1−14)×(1−15)×(1−16)×(1−17)×(1−18)×(1−19)×(1−110)\left(1 - \frac{1}{2}\right) \times \left(1 - \frac{1}{3}\right) \times \left(1 - \frac{1}{4}\right) \times \left(1 - \frac{1}{5}\right) \times \left(1 - \frac{1}{6}\right) \times \left(1 - \frac{1}{7}\right) \times \left(1 - \frac{1}{8}\right) \times \left(1 - \frac{1}{9}\right) \times \left(1 - \frac{1}{10}\right)?

Make a general statement and explain.

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Frequently Asked Questions

What are the important topics in Working with Fractions for CBSE Class 7 Mathematics?
Working with Fractions covers several key topics that are frequently asked in CBSE Class 7 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Working with Fractions — CBSE Class 7 Mathematics?
Understand the core concepts first, then work through the 43 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
Where can I get free NCERT Solutions for Working with Fractions Class 7 Mathematics?
This page has free step-by-step NCERT Solutions for every exercise question in Working with Fractions (CBSE Class 7 Mathematics) — written the way examiners award marks: given, formula, working, answer.

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