---
title: "NCERT Solutions Class 7 Maths Chapter 8 Working with Fractions"
url: https://www.swavid.com/maths/class/7/chapter/working-with-fractions/ncert-solutions
dateModified: 2026-10-07T15:07:31+00:00
---

# NCERT Solutions Class 7 Maths Chapter 8 Working with Fractions

This chapter focuses on the multiplication and division of fractions, covering concepts like reciprocals, lowest form, and word problems involving fractional quantities. It builds foundational arithmetic skills for working with rational numbers through practical applications and historical contexts.

Free PDF (15 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-7/swavid-ncert-solutions-class-7-maths-chapter-8-working-with-fractions-5978f775f5.pdf

## Figure it Out

### Question 1

*3 marks · Short answer*

Tenzin drinks $\frac{1}{2}$ 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?

**Part (i)**

1. Given: Quantity of milk Tenzin drinks in 1 day = $\frac{1}{2}$ glass.
2. Number of days in a week = 7.
3. Total milk in a week = $7 \times \frac{1}{2} = \frac{7}{2}$ glasses.

Answer (i): $\frac{7}{2}$ glasses

**Part (ii)**

1. Given: Number of days in the month of January = 31 days.
2. Total milk in January = $31 \times \frac{1}{2}$ glasses.
3. Calculating the product gives $\frac{31}{2}$ glasses.

Answer (ii): $\frac{31}{2}$ glasses

**Answer:** Tenzin drinks $\frac{7}{2}$ glasses of milk in a week and $\frac{31}{2}$ glasses of milk in January.

> Common mistake: Multiplying incorrectly by treating days as fractions instead of multiplying the whole number of days by the daily fraction.

### Question 2

*1 mark · Fill in the blank*

A team of workers can make $1\text{ km}$ of a water canal in $8\text{ days}$. So, in one day, the team can make ___ $\text{km}$ of the water canal. If they work $5\text{ days}$ a week, they can make ___ $\text{km}$ of the water canal in a week.

**Solution**

1. Length of water canal made in 1 day = $\frac{1}{8}\text{ km}$.
2. Length of water canal made in 5 days = $5 \times \frac{1}{8} = \frac{5}{8}\text{ km}$.

**Answer:** $\frac{1}{8}$, $\frac{5}{8}$

> Common mistake: Writing the numerator and denominator in reverse order.

### Question 3

*3 marks · Short answer*

Manju and two of her neighbours buy $5\text{ litres}$ 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 $4\text{ weeks}$?

**Part (i)**

1. Total quantity of oil bought by Manju and her two neighbours (making $3$ families in total) is $5\text{ litres}$ every week.
2. Since they share the oil equally among the $3$ families, the share of each family in a week is $\frac{5}{3}\text{ litres}$.

Answer (i): \frac{5}{3}\text{ litres}

**Part (ii)**

1. The oil obtained by one family in $1\text{ week}$ is $\frac{5}{3}\text{ litres}$.
2. The oil obtained by one family in $4\text{ weeks}$ is $4 \times \frac{5}{3}\text{ litres} = \frac{20}{3}\text{ litres}$.

Answer (ii): \frac{20}{3}\text{ litres}

**Answer:** Each family gets $\frac{5}{3}$ litres in a week and $\frac{20}{3}$ litres in $4$ weeks.

> Common mistake: Dividing by $2$ instead of $3$ for the number of families, or adding instead of multiplying for the $4$-week total.

### Question 4

*3 marks · Short answer*

Safia saw the Moon setting on Monday at $10\text{ pm}$. Her mother, who is a scientist, told her that every day the Moon sets $\frac{5}{6}$ hour later than the previous day. How many hours after $10\text{ pm}$ will the moon set on Thursday?

**Solution**

1. Given: The Moon sets $\frac{5}{6}$ hour later each day, and Monday to Thursday is a gap of 3 days ($3 - 0 = 3$).
2. Total time later the moon sets on Thursday = $3 \times \frac{5}{6}\text{ hours}$.
3. Calculating the product: $3 \times \frac{5}{6} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2}\text{ hours}$.

**Answer:** $2\frac{1}{2}$ hours after $10\text{ pm}$

> Common mistake: Counting 4 days instead of 3 days between Monday and Thursday.

### Question 5

*3 marks · Short answer*

Multiply and then convert it into a mixed fraction:
(a) $7 \times \frac{3}{5}$
(b) $4 \times \frac{1}{3}$
(c) $\frac{9}{7} \times 6$
(d) $\frac{13}{11} \times 6$

**Part (a)**

1. $7 \times \frac{3}{5} = \frac{21}{5}$
2. Converting to mixed fraction gives $4\frac{1}{5}$.

Answer (a): $4\frac{1}{5}$

**Part (b)**

1. $4 \times \frac{1}{3} = \frac{4}{3}$
2. Converting to mixed fraction gives $1\frac{1}{3}$.

Answer (b): $1\frac{1}{3}$

**Part (c)**

1. $\frac{9}{7} \times 6 = \frac{54}{7}$
2. Converting to mixed fraction gives $7\frac{5}{7}$.

Answer (c): $7\frac{5}{7}$

**Part (d)**

1. $\frac{13}{11} \times 6 = \frac{78}{11}$
2. Converting to mixed fraction gives $7\frac{1}{11}$.

Answer (d): $7\frac{1}{11}$

**Answer:** (a) $4\frac{1}{5}$, (b) $1\frac{1}{3}$, (c) $7\frac{5}{7}$, (d) $7\frac{1}{11}$

> Common mistake: Multiplying both numerator and denominator by the whole number.

## Figure it Out

### Question 1

*3 marks · Short answer*

Find the following products. Use a unit square as a whole for representing the fractions:
(a) $\frac{1}{3} \times \frac{1}{5}$
(b) $\frac{1}{4} \times \frac{1}{3}$
(c) $\frac{1}{5} \times \frac{1}{2}$
(d) $\frac{1}{6} \times \frac{1}{5}$
Now, find $\frac{1}{12} \times \frac{1}{18}$.

**Part (a)**

1. Multiply the numerators and denominators as $\frac{1 \times 1}{3 \times 5}$.
2. The product is $\frac{1}{15}$.

Answer (a): $\frac{1}{15}$

**Part (b)**

1. Multiply the numerators and denominators as $\frac{1 \times 1}{4 \times 3}$.
2. The product is $\frac{1}{12}$.

Answer (b): $\frac{1}{12}$

**Part (c)**

1. Multiply the numerators and denominators as $\frac{1 \times 1}{5 \times 2}$.
2. The product is $\frac{1}{10}$.

Answer (c): $\frac{1}{10}$

**Part (d)**

1. Multiply the numerators and denominators as $\frac{1 \times 1}{6 \times 5}$.
2. The product is $\frac{1}{30}$.

Answer (d): $\frac{1}{30}$

**Part (e)**

1. Multiply the two unit fractions $\frac{1}{18} \times \frac{1}{12}$ by taking the product of their denominators.
2. The product is $\frac{1}{18 \times 12} = \frac{1}{216}$.

Answer (e): $\frac{1}{216}$

**Answer:** (a) $\frac{1}{15}$, (b) $\frac{1}{12}$, (c) $\frac{1}{10}$, (d) $\frac{1}{30}$, and $\frac{1}{216}$

> Common mistake: Adding the denominators instead of multiplying them when finding the product of fractional units.

### Question 2

*3 marks · Short answer*

Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations.
(a) $\frac{2}{3} \times \frac{4}{5}$
(b) $\frac{1}{4} \times \frac{2}{3}$
(c) $\frac{3}{5} \times \frac{1}{2}$
(d) $\frac{4}{6} \times \frac{3}{5}$

**Part (a)**

1. Multiply the numerators and denominators: $\frac{2 \times 4}{3 \times 5}$.
2. Calculate the product to get $\frac{8}{15}$.

Answer (a): $\frac{8}{15}$

**Part (b)**

1. Multiply the numerators and denominators: $\frac{1 \times 2}{4 \times 3} = \frac{2}{12}$.
2. Simplify by dividing the numerator and denominator by their common factor $2$ to get $\frac{1}{6}$.

Answer (b): $\frac{1}{6}$

**Part (c)**

1. Multiply the numerators and denominators: $\frac{3 \times 1}{5 \times 2}$.
2. Calculate the product to get $\frac{3}{10}$.

Answer (c): $\frac{3}{10}$

**Part (d)**

1. Multiply the numerators and denominators: $\frac{4 \times 3}{6 \times 5} = \frac{12}{30}$.
2. Simplify by dividing the numerator and denominator by their common factor $6$ to get $\frac{2}{5}$.

Answer (d): $\frac{2}{5}$

**Answer:** (a) $\frac{8}{15}$, (b) $\frac{1}{6}$, (c) $\frac{3}{10}$, (d) $\frac{2}{5}$

> Common mistake: Failing to reduce fractions to their lowest terms at the end.

## Figure it Out

### Question 1

*5 marks · Case-based*

A water tank is filled from a tap. If the tap is open for $1\text{ hour}$, $\frac{7}{10}$ of the tank gets filled. How much of the tank is filled if the tap is open for
(a) $\frac{1}{3}$ hour ____________
(b) $\frac{2}{3}$ hour ____________
(c) $\frac{3}{4}$ hour ____________
(d) $\frac{7}{10}$ hour ____________
(e) For the tank to be full, how long should the tap be running?

**Part (a)**

1. Part of the tank filled in $1\text{ hour}$ is $\frac{7}{10}$.
2. Multiplying by the time $\frac{1}{3}\text{ hour}$, we get $\frac{1}{3} \times \frac{7}{10} = \frac{7}{30}$.

Answer (a): $\frac{7}{30}\text{ part}$

**Part (b)**

1. Part of the tank filled in $1\text{ hour}$ is $\frac{7}{10}$.
2. Multiplying by the time $\frac{2}{3}\text{ hour}$, we get $\frac{2}{3} \times \frac{7}{10} = \frac{14}{30}\text{ part}$.

Answer (b): $\frac{14}{30}\text{ part}$

**Part (c)**

1. Part of the tank filled in $1\text{ hour}$ is $\frac{7}{10}$.
2. Multiplying by the time $\frac{3}{4}\text{ hour}$, we get $\frac{3}{4} \times \frac{7}{10} = \frac{21}{40}\text{ part}$.

Answer (c): $\frac{21}{40}\text{ part}$

**Part (d)**

1. Part of the tank filled in $1\text{ hour}$ is $\frac{7}{10}$.
2. Multiplying by the time $\frac{7}{10}\text{ hour}$, we get $\frac{7}{10} \times \frac{7}{10} = \frac{49}{100}\text{ part}$.

Answer (d): $\frac{49}{100}\text{ part}$

**Part (e)**

1. To fill $1\text{ complete tank}$ at the rate of $\frac{7}{10}\text{ of the tank per hour}$, we divide $1$ by $\frac{7}{10}$.
2. Using reciprocal, $1 \div \frac{7}{10} = 1 \times \frac{10}{7} = \frac{10}{7}\text{ hours}$.

Answer (e): $\frac{10}{7}\text{ hours}$

**Answer:** Filled portions are (a) $\frac{7}{30}$, (b) $\frac{14}{30}$, (c) $\frac{21}{40}$, (d) $\frac{49}{100}$, and time to fill the tank is $\frac{10}{7}\text{ hours}$

> Common mistake: Multiplying instead of dividing when finding the total time required for a full tank.

### Question 2

*3 marks · Case-based*

The government has taken $\frac{1}{6}$ of Somu's land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and $\frac{1}{3}$ 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?

**Part (a)**

1. The part of land remaining with Somu after taking $\frac{1}{6}$ is $1 - \frac{1}{6} = \frac{5}{6}$.
2. Krishna gets half of the remaining part, which is $\frac{1}{2} \times \frac{5}{6} = \frac{5}{12}$.

Answer (a): $\frac{5}{12}$ of the original land

**Part (b)**

1. The part of land remaining with Somu is $\frac{5}{6}$.
2. Bora gets $\frac{1}{3}$ of the remaining part, which is $\frac{1}{3} \times \frac{5}{6} = \frac{5}{18}$.

Answer (b): $\frac{5}{18}$ of the original land

**Part (c)**

1. The shares given away are $\frac{5}{12}$ to Krishna and $\frac{5}{18}$ to Bora. Their sum is $\frac{5}{12} + \frac{5}{18} = \frac{15 + 10}{36} = \frac{25}{36}$.
2. The land kept by Somu for herself is the remaining part $\frac{5}{6} - \frac{25}{36} = \frac{30 - 25}{36} = \frac{5}{36}$.

Answer (c): $\frac{5}{36}$ of the original land

**Answer:** Krishna got $\frac{5}{12}$, Bora got $\frac{5}{18}$, and Somu kept $\frac{5}{36}$ of the original land.

> Common mistake: Taking fractions of the original land directly instead of fractions of the remaining land.

### Question 3

*3 marks · Short answer*

Find the area of a rectangle of sides $3\frac{3}{4}\text{ ft}$ and $9\frac{3}{5}\text{ ft}$.

**Solution**

1. Sides are 3 3/4 ft = 15/4 ft and 9 3/5 ft = 48/5 ft
2. Area = 15/4 * 48/5
3. Area = (15 * 48) / (4 * 5) = 3 * 12 = 36 sq. ft.

**Answer:** 36 sq. ft.

> Common mistake: Forgetting to convert mixed fractions to improper fractions before multiplying.

### Question 4

*3 marks · Short answer*

Tsewang plants four saplings in a row in his garden. The distance between two saplings is $\frac{3}{4}\text{ m}$. Find the distance between the first and last sapling. [Hint: Draw a rough diagram with four saplings with distance between two saplings as $\frac{3}{4}\text{ m}$]

**Solution**

1. There are 4 saplings, so there are 3 gaps between them.
2. Distance = 3 * 3/4 m
3. Distance = 9/4 m = 2 1/4 m

**Answer:** 2 1/4 m

> Common mistake: Multiplying by 4 instead of 3 gaps.

### Question 5

*3 marks · Short answer*

Which is heavier: $\frac{12}{15}$ of $500\text{ grams}$ or $\frac{3}{20}$ of $4\text{ kg}$?

**Solution**

1. First quantity = $\frac{12}{15} \times 500\text{ g} = \frac{12 \times 500}{15} = \frac{6000}{15} = 400\text{ g}$.
2. Second quantity = $\frac{3}{20} \times 4\text{ kg} = \frac{3}{20} \times 4000\text{ g} = \frac{3 \times 4000}{20} = \frac{12000}{20} = 600\text{ g}$.
3. Comparing the two weights, $600\text{ g}$ is greater than $400\text{ g}$, so $\frac{3}{20}$ of $4\text{ kg}$ is heavier.

**Answer:** $\frac{3}{20}$ of $4\text{ kg}$ is heavier.

> Common mistake: Forgetting to convert $4\text{ kg}$ into grams before multiplying, or confusing the values.

## Figure it Out

### Question 1

*3 marks · Short answer*

Evaluate the following:
- $3 \div \frac{7}{9}$
- $\frac{14}{4} \div 2$
- $\frac{2}{3} \div \frac{2}{3}$
- $\frac{14}{6} \div \frac{7}{3}$
- $\frac{4}{3} \div \frac{3}{4}$
- $\frac{7}{4} \div \frac{1}{7}$
- $\frac{8}{2} \div \frac{4}{15}$
- $\frac{1}{5} \div \frac{1}{9}$
- $\frac{1}{6} \div \frac{11}{12}$
- $3\frac{2}{3} \div 1\frac{3}{8}$

**Part (a)**

1. $3 \div \frac{7}{9} = 3 \times \frac{9}{7}$
2. $= \frac{27}{7}$

Answer (a): $\frac{27}{7}$

**Part (b)**

1. $\frac{14}{4} \div 2 = \frac{14}{4} \times \frac{1}{2}$
2. $= \frac{14}{8} = \frac{7}{4}$

Answer (b): $\frac{7}{4}$

**Part (c)**

1. $\frac{2}{3} \div \frac{2}{3} = \frac{2}{3} \times \frac{3}{2}$
2. $= \frac{6}{6} = 1$

Answer (c): $1$

**Part (d)**

1. $\frac{14}{6} \div \frac{7}{3} = \frac{14}{6} \times \frac{3}{7}$
2. $= \frac{42}{42} = 1$

Answer (d): $1$

**Part (e)**

1. $\frac{4}{3} \div \frac{3}{4} = \frac{4}{3} \times \frac{4}{3}$
2. $= \frac{16}{9}$

Answer (e): $\frac{16}{9}$

**Part (f)**

1. $\frac{7}{4} \div \frac{1}{7} = \frac{7}{4} \times \frac{7}{1}$
2. $= \frac{49}{4}$

Answer (f): $\frac{49}{4}$

**Part (g)**

1. $\frac{8}{2} \div \frac{4}{15} = \frac{8}{2} \times \frac{15}{4}$
2. $= \frac{120}{8} = 15$

Answer (g): $15$

**Part (h)**

1. $\frac{1}{5} \div \frac{1}{9} = \frac{1}{5} \times \frac{9}{1}$
2. $= \frac{9}{5}$

Answer (h): $\frac{9}{5}$

**Part (i)**

1. $\frac{1}{6} \div \frac{11}{12} = \frac{1}{6} \times \frac{12}{11}$
2. $= \frac{12}{66} = \frac{2}{11}$

Answer (i): $\frac{2}{11}$

**Part (j)**

1. $3\frac{2}{3} \div 1\frac{3}{8} = \frac{11}{3} \div \frac{11}{8}$
2. $= \frac{11}{3} \times \frac{8}{11} = \frac{8}{3} = 2\frac{2}{3}$

Answer (j): $2\frac{2}{3}$

**Answer:** Evaluated all ten division expressions using the reciprocal method.

> Common mistake: Forgetting to invert the divisor fraction before multiplying.

### Question 2

*1 mark · MCQ*

For each of the questions below, choose the expression that describes the solution. Then simplify it.
(a) Maria bought $8\text{ m}$ of lace to decorate the bags she made for school. She used $\frac{1}{4}\text{ m}$ for each bag and finished the lace. How many bags did she decorate?
(b) $\frac{1}{2}\text{ meter}$ of ribbon is used to make $8$ badges. What is the length of the ribbon used for each badge?
(c) A baker needs $\frac{1}{6}\text{ kg}$ of flour to make one loaf of bread. He has $5\text{ kg}$ of flour. How many loaves of bread can he make?

- $8 \times \frac{1}{4}$
- $\frac{1}{8} \times \frac{1}{4}$
- $8 \div \frac{1}{4}$
- $\frac{1}{4} \div 8$
- $8 \times \frac{1}{2}$
- $\frac{1}{2} \div \frac{1}{8}$
- $8 \div \frac{1}{2}$
- $\frac{1}{2} \div 8$
- $5 \times \frac{1}{6}$
- $\frac{1}{6} \div 5$
- $5 \div \frac{1}{6}$
- $5 \times 6$

**Part (a)**

1. Total lace is 8 m and each bag uses 1/4 m.
2. Number of bags = $8 \div \frac{1}{4}$.

Answer (a): (iii) $8 \div \frac{1}{4}$

**Part (b)**

1. Total ribbon is 1/2 m used for 8 badges.
2. Length per badge = $\frac{1}{2} \div 8$.

Answer (b): (iv) $\frac{1}{2} \div 8$

**Part (c)**

1. Total flour is 5 kg and each loaf needs 1/6 kg.
2. Number of loaves = $5 \div \frac{1}{6}$.

Answer (c): (iii) $5 \div \frac{1}{6}$

**Answer:** The correct expressions are (a)(iii), (b)(iv), and (c)(iii).

> Common mistake: Confusing the dividend and divisor in word problems.

### Question 3

*3 marks · Short answer*

If $\frac{1}{4}\text{ kg}$ of flour is used to make $12$ rotis, how much flour is used to make $6$ rotis?

**Solution**

1. Given: $\frac{1}{4}$ kg flour makes 12 rotis.
2. Flour for 1 roti = $\frac{1}{4} \div 12 = \frac{1}{4} \times \frac{1}{12} = \frac{1}{48}$ kg.
3. Flour for 6 rotis = $6 \times \frac{1}{48} = \frac{6}{48} = \frac{1}{8}$ kg.

**Answer:** $\frac{1}{8}$ kg

> Common mistake: Multiplying instead of dividing to find the flour for one roti.

### Question 4

*3 marks · Short answer*

Pāṭīgaṇita, a book written by Sridharacharya in the 9th century CE, mentions this problem: "Friend, after thinking, what sum will be obtained by adding together $1 \div \frac{1}{6}$, $1 \div \frac{1}{10}$, $1 \div \frac{1}{13}$, $1 \div \frac{1}{9}$, and $1 \div \frac{1}{2}$". What should the friend say?

**Solution**

1. The problem asks for the sum of $1 \div \frac{1}{6}$, $1 \div \frac{1}{10}$, $1 \div \frac{1}{13}$, $1 \div \frac{1}{9}$, and $1 \div \frac{1}{2}$.
2. This is equivalent to $6 + 10 + 13 + 9 + 2$.
3. Sum = $6 + 10 + 13 + 9 + 2 = 40$.

**Answer:** 40

> Common mistake: Adding the fractions instead of their reciprocals.

### Question 5

*3 marks · Short answer*

Mira is reading a novel that has $400$ pages. She read $\frac{1}{5}$ of the pages yesterday and $\frac{3}{10}$ of the pages today. How many more pages does she need to read to finish the novel?

**Solution**

1. Total number of pages in the novel is $400$.
2. Fraction of pages read yesterday is $\frac{1}{5}$ and today is $\frac{3}{10}$.
3. Total fraction of pages read = $\frac{1}{5} + \frac{3}{10} = \frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2}$.
4. Fraction of pages left to read = $1 - \frac{1}{2} = \frac{1}{2}$.
5. Number of pages left to read = $\frac{1}{2} \times 400 = 200\text{ pages}$.

**Answer:** $200\text{ pages}$

> Common mistake: Adding the fractions without finding a common denominator first.

### Question 6

*3 marks · Short answer*

A car runs $16\text{ km}$ using $1\text{ litre}$ of petrol. How far will it go using $2\frac{3}{4}\text{ litres}$ of petrol?

**Solution**

1. Given distance covered in $1\text{ litre}$ of petrol = $16\text{ km}$.
2. Given quantity of petrol used = $2\frac{3}{4}\text{ litres} = \frac{11}{4}\text{ litres}$.
3. Total distance covered = $\frac{11}{4} \times 16\text{ km}$.
4. Distance = $\frac{11 \times 16}{4} = 11 \times 4\text{ km}$.
5. Distance = $44\text{ km}$.

**Answer:** $44\text{ km}$

> Common mistake: Failing to convert the mixed fraction into an improper fraction before multiplying.

### Question 7

*3 marks · Short answer*

Amritpal decides on a destination for his vacation. If he takes a train, it will take him $5\frac{1}{6}\text{ hours}$ to get there. If he takes a plane, it will take him $\frac{1}{2}\text{ hour}$. How many hours does the plane save?

**Solution**

1. Time taken by train = $5\frac{1}{6}\text{ hours} = \frac{31}{6}\text{ hours}$.
2. Time taken by plane = $\frac{1}{2}\text{ hour} = \frac{3}{6}\text{ hours}$.
3. Time saved = $\frac{31}{6} - \frac{3}{6} = \frac{28}{6}\text{ hours} = \frac{14}{3}\text{ hours} = 4\frac{2}{3}\text{ hours}$.
4. The plane saves $4\frac{2}{3}\text{ hours}$.

**Answer:** $4\frac{2}{3}\text{ hours}$ (or $\frac{14}{3}\text{ hours}$)

> Common mistake: Subtracting incorrectly without converting fractions to a common denominator.

### Question 8

*3 marks · Short answer*

Mariam's grandmother baked a cake. Mariam and her cousins finished $\frac{4}{5}$ of the cake. The remaining cake was shared equally by Mariam's three friends. How much of the cake did each friend get?

**Solution**

1. Remaining part of the cake = $1 - \frac{4}{5} = \frac{1}{5}$
2. The remaining cake is shared equally among 3 friends, so each friend gets $\frac{1}{5} \div 3$
3. Calculation: $\frac{1}{5} \times \frac{1}{3} = \frac{1}{15}$ of the whole cake

**Answer:** $\frac{1}{15}$ of the whole cake

> Common mistake: Dividing the total cake instead of the remaining cake among the three friends.

### Question 9

*1 mark · MCQ*

Choose the option(s) describing the product of ($\frac{565}{465} \times \frac{707}{676}$):

- > \frac{565}{465}
- < \frac{565}{465}
- > \frac{707}{676}
- < \frac{707}{676}
- > 1
- < 1

**Solution**

1. Both fractions $\frac{565}{465}$ and $\frac{707}{676}$ are greater than 1 because their numerators are greater than their denominators.
2. When two numbers greater than 1 are multiplied, the product is greater than both numbers and greater than 1.
3. Therefore, options (a), (c), and (e) are correct.

**Answer:** (a), (c) and (e) are correct.

> Common mistake: Thinking that multiplying two fractions always results in a number smaller than the given numbers.

### Question 10

*3 marks · Short answer*

What fraction of the whole square is shaded?

**Solution**

1. As seen in the figure in the textbook, the big square is divided into a red square of area $\frac{1}{4}$ square units.
2. The yellow triangle inside it has an area of $\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$ square units.
3. The shaded region occupies $\frac{3}{4}$ of the yellow triangle, giving an area of $\frac{3}{4} \times \frac{1}{8} = \frac{3}{32}$ of the whole square.

**Answer:** $\frac{3}{32}$ of the whole square

> Common mistake: Miscounting the grid subdivisions and total equal parts.

### Question 11

*3 marks · Short answer*

A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in the 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?

**Solution**

1. At each split point, the group of ants divides equally into two, which is multiplication by $\frac{1}{2}$.
2. By tracing the path to the mango tree and sugarcane field as shown in Fig. 8.7, we multiply the fractional splits along the branches.
3. The fraction reaching the mango tree is $\frac{29}{32}$ and the fraction reaching the sugarcane field is $\frac{3}{32}$.

**Answer:** Mango tree: $\frac{29}{32}$, Sugarcane field: $\frac{3}{32}$

> Common mistake: Incorrectly counting the number of splits along each path.

### Question 12

*3 marks · Short answer*

What is $1 - \frac{1}{2}$?
$(1 - \frac{1}{2}) \times (1 - \frac{1}{3})$?
$(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times (1 - \frac{1}{5})$?
$(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times (1 - \frac{1}{5}) \times (1 - \frac{1}{6}) \times (1 - \frac{1}{7}) \times (1 - \frac{1}{8}) \times (1 - \frac{1}{9}) \times (1 - \frac{1}{10})$?
Make a general statement and explain.

**Solution**

1. Evaluate step by step: $1 - \frac{1}{2} = \frac{1}{2}$
2. Next products give $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$, and continuing this cancellation leaves only the first numerator and last denominator.
3. The general statement is $(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times \dots \times (1 - \frac{1}{n}) = \frac{1}{n}$.

**Answer:** $\frac{1}{n}$

> Common mistake: Failing to recognize the telescoping cancellation of numerators and denominators.

## Frequently asked questions

### How many exercises or questions are there in NCERT Class 7 Maths Chapter 8 Working with Fractions?

This chapter in the new NCERT book for the 2026-27 session contains four sets of Figure it Out exercises with a total of 24 questions. SwaVid's free PDF and step-by-step solutions are on this page only to help you practice every single question easily.

### What topics do the questions in this chapter cover?

The questions cover concepts such as fraction as division, multiplication and division of fractions, mixed fractions, addition and subtraction, and finding the area of shaded regions using unit squares. SwaVid's free PDF and step-by-step solutions are on this page only to help you master all these topics.

### Which are the hardest question types in this chapter and how do I approach them?

Case-based questions involving fractions of a remaining quantity and tree diagrams can be challenging. You should approach them by breaking down the word problem step by step into smaller multiplication or division statements.

### How should I write answers to get full marks in Class 7 Maths Chapter 8?

To secure full marks, always write down the given values clearly, show the step-by-step conversion of mixed fractions to improper fractions where needed, and state the final units. SwaVid's free PDF and step-by-step solutions are on this page only to show you the exact presentation style required.

### Is the free PDF for Working with Fractions available for the 2026-27 session?

Yes, complete solutions aligned with the new NCERT book based on the NCF 2023 guidelines are provided here. SwaVid's free PDF and step-by-step solutions are on this page only to support your exam preparation without any hassle.

## Related pages

- [Class 7 Maths chapters](https://www.swavid.com/maths/class/7)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student