Class 7 Maths Chapter 8 Solutions: Working with Fractions

NCERT Class 7 Maths Chapter 8 Working with Fractions Solutions Question Answer

Figure it Out (Pages 176-177)

1. Tenzin drinks 1/2 glass of milk every day. How many glasses of milk does he drink in a week? In January?

Answer: In one week, there are 7 days. So, total milk = $7 \times \frac{1}{2} = \frac{7}{2} = 3\frac{1}{2}$ glasses. In January, which has 31 days, total milk = $31 \times \frac{1}{2} = \frac{31}{2} = 15\frac{1}{2}$ glasses.

2. A team of workers can make 1 km of water canal in 8 days. In one day, they can make ___ km. Working 5 days a week, they can make ___ km in a week.

Answer: In one day, they make $1 \div 8 = \frac{1}{8}$ km. In 5 days, $5 \times \frac{1}{8} = \frac{5}{8}$ km.

3. Manju and two neighbours buy 5 litres of oil every week and share equally among 3 families. How much does each family get in a week? How much in 4 weeks?

Answer: Each family gets $5 \div 3 = \frac{5}{3} = 1\frac{2}{3}$ litres in a week. In 4 weeks: $4 \times \frac{5}{3} = \frac{20}{3} = 6\frac{2}{3}$ litres.

4. Safia saw the Moon setting Monday at 10 pm. Moon sets 5/6 hour later each day. How many hours after 10 pm will it set on Thursday?

Answer: From Monday to Thursday is 3 days. So, time after 10 pm = $3 \times \frac{5}{6} = \frac{15}{6} = 2\frac{1}{2}$ hours. On Thursday, Moon sets at 12:30 am (10 pm + $2\frac{1}{2}$ hours).

5. Multiply and convert to mixed fraction:

1. $7 \times \frac{3}{5} = \frac{21}{5} = 4\frac{1}{5}$
2. $4 \times \frac{1}{3} = \frac{4}{3} = 1\frac{1}{3}$
3. $\frac{9}{7} \times 6 = \frac{54}{7} = 7\frac{5}{7}$
4. $\frac{13}{11} \times 6 = \frac{78}{11} = 7\frac{1}{11}$

Figure it Out (Pages 180-181)

1. Find:

• $\frac{1}{3} \times \frac{1}{5} = \frac{1}{15}$
• $\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$
• $\frac{1}{5} \times \frac{1}{2} = \frac{1}{10}$
• $\frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$
• $\frac{1}{12} \times \frac{1}{18} = \frac{1}{216}$

2. Find:

• $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$
• $\frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}$
• $\frac{3}{5} \times \frac{1}{2} = \frac{3}{10}$
• $\frac{4}{6} \times \frac{3}{5} = \frac{2}{3} \times \frac{3}{5} = \frac{2 \times 3}{3 \times 5} = \frac{2}{5}$

Figure it Out (Pages 183-184)

1. A tap fills 7/10 of a tank in 1 hour. How much in:

1. 1/3 hour: $7/10 \times 1/3 = 7/30$ of tank
2. 2/3 hour: $7/10 \times 2/3 = 14/30 = 7/15$ of tank
3. 3/4 hour: $7/10 \times 3/4 = 21/40$ of tank
4. 7/10 hour: $7/10 \times 7/10 = 49/100$ of tank
5. For full tank: $1 \div (7/10) = 10/7$ hours

2. The government takes 1/6 of Somu’s land. She gives half the remainder to Krishna, 1/3 to Bora, keeps the rest.
How much, of the original land, did Krishna get? Bora? How much did Somu keep?

Answer:

• Land after government = $1 - 1/6 = 5/6$
• Krishna gets half = $1/2 \times 5/6 = 5/12$
• Remainder = $5/6 - 5/12 = 5/12$
• Bora gets $1/3$ of $5/6$ = $5/18$
• Somu keeps = $5/6 - 5/12 - 5/18 = (30-15-10)/36 = 5/36$

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

Answer: $3\frac{3}{4} = 15/4$ ft, $9\frac{3}{5} = 48/5$ ft; Area = $15/4 \times 48/5 = (15 \times 48)/(4 \times 5) = 720/20 = 36$ sq ft.

4. Tsewang plants 4 saplings, spacing 3/4 m. Distance between first and last saplings?

Answer: There are 3 gaps between 4 saplings. So total distance = $3 \times 3/4 = 9/4 = 2\frac{1}{4}$ m.

5. Which is heavier: 12/15 of 500 g or 3/20 of 4 kg?

Answer: $12/15 \times 500 = 400$ g;
$4$ kg $= 4000$ g; $3/20 \times 4000 = 600$ g.
So, $3/20$ of 4 kg (600 g) is heavier.

Is the Product Always Greater than the Numbers Multiplied?

Situation	Multiplication	Relationship
Both numbers > 1	$\frac{4}{3} \times 4 = \frac{16}{3}$	Product > both numbers
Both numbers between 0 and 1	$\frac{3}{4} \times \frac{2}{5} = \frac{3}{10}$	Product < both numbers
One between 0 and 1, one > 1	$\frac{3}{4} \times 5 = \frac{15}{4}$	Product is less than the number > 1, and greater than the number between 0 and 1

When one number is between 0 and 1, the product is less than the other number. When one number is greater than 1, the product is greater than the other number.

8.2 Division of Fractions

1. What is $1 \div \frac{2}{3}$?

Answer: $1 \div \frac{2}{3} = 1 \times \frac{3}{2} = \frac{3}{2}$

2. What is $3 \div \frac{2}{3}$?

Answer: $3 \div \frac{2}{3} = 3 \times \frac{3}{2} = \frac{9}{2}$

3. What is $\frac{1}{5} \div \frac{1}{2}$?

Answer: $\frac{1}{5} \div \frac{1}{2} = \frac{1}{5} \times \frac{2}{1} = \frac{2}{5}$

4. What is $\frac{2}{3} \div \frac{3}{5}$?

Answer: $\frac{2}{3} \div \frac{3}{5} = \frac{2}{3} \times \frac{5}{3} = \frac{10}{9}$

Dividend, Divisor and Quotient:

• $6 \div 3 = 2$, $2 < 6$
• $6 \div \frac{1}{4} = 24$, $24 > 6$
• $\frac{1}{8} \div \frac{1}{4} = \frac{1}{2}, \frac{1}{2} > \frac{1}{8}$

8.3 Some Problems Involving Fractions

Example 3: Leena made 5 cups of tea using $1/4$ litre of milk. How much milk in each cup?

Answer: $1/4 \div 5 = 1/20$ litre per cup.

Example 4: Baudhāyana’s Śhulbasūtra: Cover area $7\frac{1}{2}=15/2$ units with square bricks of side $1/5$:

Answer: Area per brick = $1/5 \times 1/5 = 1/25$. Number of bricks = $15/2 \div 1/25 = 25 \times 15/2 = 375/2$.

Example 5: Chaturveda Pṛithūdakasvāmī: Four fountains fill a cistern:

• First: 1 day $1 \div 1 = 1$
• Second: $1 \div 1/2 = 2$
• Third: $1 \div 1/4 = 4$
• Fourth: $1 \div 1/5 = 5$

Together, $1+2+4+5=12$; so they fill it in $1/12$ day.

Figure it Out (Pages 196-198)

1. Evaluate the following (find the quotient):

1. $3 \div \frac{7}{9} = 3 \times \frac{9}{7} = \frac{27}{7}$
2. $\frac{14}{4} \div 2 = \frac{14}{4} \times \frac{1}{2} = \frac{14}{8} = \frac{7}{4}$
3. $\frac{2}{3} \div \frac{2}{3} = 1$
4. $\frac{14}{6} \div \frac{7}{3} = \frac{14}{6} \times \frac{3}{7} = \frac{42}{42} = 1$
5. $3 \div \frac{3}{4} = 3 \times \frac{4}{3} = 4$
6. $\frac{7}{4} \div \frac{1}{7} = \frac{7}{4} \times 7 = \frac{49}{4}$
7. $\frac{8}{2} \div \frac{4}{15} = 4 \times \frac{15}{4} = 15$
8. $\frac{1}{5} \div \frac{1}{9} = \frac{1}{5} \times 9 = \frac{9}{5}$
9. $\frac{1}{6} \div \frac{11}{12} = \frac{1}{6} \times \frac{12}{11} = \frac{2}{11}$
10. $3\frac{2}{3} \div 1\frac{3}{8} = \frac{11}{3} \div \frac{11}{8} = \frac{11}{3} \times \frac{8}{11} = \frac{8}{3} = 2\frac{2}{3}$

2. Choose the correct expression:

• Maria bought 8 m lace, used $1/4$ m/bag, finished the lace. How many bags? $8 \div 1/4$
• $1/2$ m ribbon used to make 8 badges. Ribbon/badge? $1/2 \div 8$
• Baker needs $1/6$ kg/loaf; has 5 kg. Number of loaves? $5 \div 1/6$

3. If $1/4$ kg flour is used for 12 rotis, how much for 6 rotis?

Answer: $1/4 \div 12 = 1/48$ kg for 1 roti; for 6 rotis: $6 \times 1/48 = 1/8$ kg.

4. Sridharacharya (9th c.): "What is $1\div 1/6 + 1\div 1/10 + 1 \div 1/13 + 1 \div 1/9 + 1 \div 1/2$"?

Answer: $1\div 1/6 = 6; 1\div 1/10 = 10; 1\div 1/13 = 13; 1\div 1/9 = 9; 1\div 1/2 = 2$. Sum = $6+10+13+9+2=40$.

5. Mira reading 400-page novel, read $1/5$ yesterday, $3/10$ today. Pages left?

Answer: $1/5+3/10 = 2/10+3/10=5/10=1/2$ read. Pages left = $1/2$ of 400 = 200 pages.

6. Car runs 16 km/litre. How far on $2\frac{3}{4}$ litres?

Answer: $2\frac{3}{4}=11/4$ litres. $16 \times 11/4 = 44$ km.

7. Holiday: Train = $5\frac{1}{6}$ hrs, Plane = $1/2$ hr. How much faster is plane?

Answer: Time saved = $5\frac{1}{6} - 1/2 = 31/6 - 3/6 = 28/6 = 14/3 = 4\frac{2}{3}$ hours.

8. Mariam’s cousins finished $4/5$ of cake. Remainder shared by 3 friends. How much did each get?

Answer: Remainder = $1 - 4/5 = 1/5$. Each gets $1/5 \div 3 = 1/15$ of cake.

9. Which is true about ($565/465 \times 707/676$):

Answer: $565/465 = 1.215$, $707/676 = 1.0459$. $565/465 \times 707/676 = 859/572 \approx 1.501$. So, it's greater than both numbers and greater than 1.

10. What is $1 - 1/2$?

Answer: $1-1/2=1/2$

(1 - 1/2) × (1 - 1/3)?

Answer: $(1-1/2) \times (1-1/3) = 1/2 \times 2/3 = 1/3$

(1-1/2) × (1-1/3) × (1-1/4) × (1-1/5)?

Answer: $1/2 \times 2/3 \times 3/4 \times 4/5 = (1/2) \times (2/3) \times (3/4) \times (4/5) = 1/5$

Mastering the Basics of Fractions in Class 7 Maths

The chapter Working with Fractions helps students understand addition, subtraction, multiplication, and division of fractions. Grasping these fundamental concepts is essential for success in higher-level Maths.

By practicing the NCERT Solutions for Class 7 Maths Chapter 8 Working with Fractions, you build a strong foundation for exams. These stepwise explanations ensure conceptual clarity and help you solve real-life fraction problems with confidence.

For the academic year 2025-26, it’s important to review all exercise-based questions. Regular revision and attention to keywords like multiplication and division will enhance your exam performance and set you on the path to scoring higher marks in Maths.