NCERT Solutions for Class 7 Maths Ganita Prakash Chapter 8 Working with Fractions

The NCERT solution for class 7 maths chapter 8 guide for "Working with Fractions" helps you learn how to multiply and divide fractions. This chapter goes from easy adding to solving real-life problems, like sharing food or measuring land. Understanding these ideas is a big part of getting high marks in your math tests and getting ready for harder math later. Fractions are not just numbers in a book; they are used in kitchens, on construction sites, and even in science labs.

Check Out: PW Class 7th Books

Figure it Out (Page 176 – 177)

NCERT Solutions for Class 7 Maths Chapter 8 Figure it Out (Page 176 – 177) are provided below with detailed step-by-step explanations. These solutions will help students practice different types of fraction-based questions and improve their understanding. Check the solved answers below to strengthen your concepts and preparation.

1. 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?
Solution:
Glass of milk drank every day = 1/2
Glasses of milk drank in a week = 1/2 × 7 = 7/2
Days in month of January = 31
Glasses of milk drank in month of January = 31 × 1/2 = 31/2 = 15 1/2

2. 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:
The length of canal made by workers in 8 days = 1 km
The length of canal made by workers in 1 day = 1/8 km
By working 5 days in a week, the length of canal made by workers = 5 × 1/8 = 5/8 km.

3. 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:
Amount of oil shared by 3 families in a week = 5 litres
Amount of oil one family got in a week = 5/3 litres
Amount of oil one family got in 4 weeks = 4 × 5/3 = 20/3 = 6 2/3 litres.

4. 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?
Solution:
No. of days from Monday to Thursday = 3
Delay in moon setting time per day = 5/6 hour
Delay in moon setting time over 3 days = 3 × 5/6 hour = 5/2 = 2.5 hours
Thus, the Moon will set 2.5 hours or 2 hours 30 minutes after 10 PM 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

Solution:
(a) 7 × 3/5 = 21/5 = 4 1/5
(b) 4 × 1/3 = 4/3
(c) 9/7 × 6 = 54/7
(d) 13/11 × 6 = 78/11

NCERT Solutions for Class 7 Maths Chapter 8 Figure it out (Page 183)

NCERT Solutions for Class 7 Maths Chapter 8 Figure it Out (Page 183) are provided below in a clear and simple format. These solutions include practical fraction-based word problems with step-by-step answers. Check the detailed Class 7 Chapter 8 solutions below to strengthen your understanding and improve exam preparation:

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?

Solution: Part of the tank filled in 1 hour = 7/10

(a) Part of the tank filled in 1/3 hour = 1/3 × 7/10 = 7/30
(b) Part of the tank filled in 2/3 hour = 2/3 × 7/10 = 14/30 = 7/15
(c) Part of the tank filled in 3/4 hour = 3/4 × 7/10 = 21/40
(d) Part of the tank filled in 7/10 hour = 7/10 × 7/10 = 49/100
(e) Part of the tank filled in 1 hour = 7/10
Time required to fill 7/10 of a tank = 1 hour
Time required to fill 1 tank = 1 × 10/7 = 10/7 hours = 1 3/7 hours.

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 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:
Part of Somu’s land acquired by the government = 1/6
Somu’s original land = 1 – 1/6 = 5/6

(a) Part of the land given to Krishna = 1/2 of original land = 1/2 × 5/6 = 5/12
(b) Part of the land given to Bora = 1/3 of original land = 1/3 × 5/6 = 5/18
(c) Part of the land Somu kept for herself = 5/6 – (5/12 + 5/18)
= 5/6 – (25/36)
= (30/36 – 25/36) = 5/36

Read More: NCERT Solutions for Class 7 Maths Chapter 1 Integers

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

Solution:
Area of rectangle = 15/4 ft × 48/5 ft = 3 × 12 = 36 sq ft

4. 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.
[Hint: Draw a rough diagram with four saplings with distance between two saplings as 3/4 m]

Solution:
No. of saplings in a row in garden = 4
Distance between two saplings = 3/4 m
Distance between first and last sapling = 3/4 + 3/4 + 3/4 = 9/4 m = 2 1/4 m

Read More: NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

NCERT Solutions for Class 7 Maths Chapter 8 Textbook Page 185

NCERT Solutions for Class 7 Maths Chapter 8 Textbook Page 185 are given below with simple and clear explanations. This section explains whether the product of two numbers is greater or less than the given numbers. Check the detailed step-by-step Class 7 Chapter 8 solutions provided below:

Is the Product Always Greater than the Numbers Multiplied?

Q. What can you conclude about the relationship between the numbers multiplied and the product? Fill in the blanks:
• When one of the numbers being multiplied is between 0 and 1, the product is __________ (greater/less) than the other number.
• When one of the numbers being multiplied is greater than 1, the product is __________ (greater/less) than the other number.

Solution:
(i) When one of the numbers being multiplied is between 0 and 1, the product is less than the other number.

Example:
Let one number be 1/4 and other number be 100.
Product = 1/4 × 100 = 25.
Hence, the product (25) is less than the other number (100).

(ii) When one of the numbers being multiplied is greater than 1, the product is greater than the other number.

Example:
Let one number be 10 and other number 50.
Product = 10 × 50 = 500.
Hence, the product (500) is greater than the other number (50).

NCERT Solutions for Class 7 Maths Chapter 8 Textbook Page 194

NCERT Solutions for Class 7 Maths Chapter 8 Textbook Page 194 are provided below with complete explanations. This section deals with solving problems on currency conversions and fractions in a step-by-step manner. Students can check the detailed Class 7 Chapter 8 solutions given here to practice effectively and prepare well:

Q. If we assume 1 gold dinar = 12 silver drammas, 1 silver dramma = 4 copper panas, 1 copper pana = 6 mashakas, and 1 pana = 30 cowrie shells,
1 copper pana = 1/48 gold dinar (1/12 × 1/4)
1 cowrie shell = ____ copper panas
1 cowrie shell = ____ gold dinar.

Solution:
1 copper pana = 1/48 gold dinar
1 copper pana = 30 cowrie shells
or 30 cowrie shells = 1 copper pana
or 1 cowrie shell = 1/30 copper panas.

or 1 cowrie shell = 1/30 × 1/48 gold dinar = 1/1440 gold dinar.

2. 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 1/4 m for each bag and finished the lace. How many bags did she decorate?
(i) 8 × 1/4
(ii) 1/8 × 1/4
(iii) 8 ÷ 1/4
(iv) 1/4 ÷ 8

Solution:
Lace bought = 8 m
Lace used to decorate one bag = 1/4 m
No. of bags decorated = 8 ÷ 1/4
So, (iii) 8 ÷ 1/4 is the correct answer.

(b) 1/2 metre of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge?
(i) 8 × 1/2
(ii) 1/2 ÷ 1/8
(iii) 8 ÷ 1/2
(iv) 1/2 ÷ 8

Solution:
Length of ribbon used to make 8 badges = 1/2 metres.
Length of ribbon used to make each badge = 1/2 ÷ 8.
So, (iv) 1/2 ÷ 8 is the correct answer.

(c) A baker needs 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 × 1/6
(ii) 1/6 ÷ 5
(iii) 5 ÷ 1/6
(iv) 5 × 6

Solution:
Quantity of flour needed to make 1 loaf of bread = 1/6 kg
Total quantity of flour = 5 kg
No. of loaves of bread made = 5 ÷ 1/6
So, (iii) 5 ÷ 1/6 is the correct answer.

4. 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?”

Solution:
The sum obtained = (1 ÷ 1/6) + (1 ÷ 1/10) + (1 ÷ 1/13) + (1 ÷ 1/9) + (1 ÷ 1/2)
= (1 × 6/1) + (1 × 10/1) + (1 × 13/1) + (1 × 9/1) + (1 × 2/1)
= 6 + 10 + 13 + 9 + 2 = 40

Therefore, the friend should say that the sum is 40.

5. 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?

Solution:
The total number of pages in the novel = 400

The number of pages read by Mira yesterday = 1/5 of 400 = 400/5 = 80 pages.
The number of pages read by Mira today = 3/10 of 400 = 120 pages.
Total pages read by Mira = 80 + 120 = 200 pages.

Therefore, the number of pages she needs to finish the novel = 400 – 200 = 200 pages.

6. A car runs 16 km using 1 litre of petrol. How far will it go using 2 3/4 litres of petrol?

Solution:
Distance travelled by car in 1 litre of petrol = 16 km.
Distance travelled by car in 2 3/4 litres of petrol = 16 × 2 3/4 = 16 × 11/4 = 4 × 11 = 44 km.

7. 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?

Solution:
The time taken by the train to reach the destination = 5 1/6 hours.
The time taken by the plane to reach the destination = 1/2 hour.

The time saved by travelling by plane = 5 1/6 – 1/2
= 31/6 – 1/2
= 31/6 – 3/6
= 28/6 = 14/3 = 4 2/3 hours.

8. 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?

Solution:
Part of cake finished by Mariam and her cousins = 4/5
Part of cake left = 1 – 4/5 = 1/5

This 1/5 part of the cake is shared equally among 3 friends.
Part each friend got = 1/5 ÷ 3 = 1/5 × 1/3 = 1/15

Thus, each of Mariam’s three friends got 1/15 of the cake.

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

Solution:
565/465 > 1 and 707/676 > 1

Since, both numbers are greater than 1, their product is greater than both the numbers.
Therefore, (a), (c) and (e) are correct options.

Read More: NCERT Solutions for Class 7 Maths Chapter 11

Learn NCERT solution for class 7 maths chapter 8

Getting ready for your math test is easy when you follow a simple plan. In this chapter, you will learn how to multiply two fractions and why the answer is always smaller than the first numbers. You will also see how to divide fractions by turning them upside down. If you practice these NCERT solution for class 7 maths chapter 8 steps, you will find it easy to solve even the hardest word problems. This chapter helps you bridge the gap between simple counting and advanced algebra.

Multiplying Fractions: The "Of" Rule

In math, the "x" sign often means the word "of." When someone asks you for half of a pizza, they are asking you to multiply. You should know these simple rules for your NCERT solutions for class 7 maths chapter 8 work.

• Fraction and a Whole Number: To multiply a fraction by a whole number, just multiply the top number (numerator) by the whole number. Keep the bottom number (denominator) the same. Think of this as repeated addition. If you have 1/4 three times, you have 1/4 + 1/4 + 1/4, which is 3/4.

• Example: If the Moon sets 5/6 hour later every day, in 3 days the delay is 3 x 5/6 = 15/6, which simplifies to 2 and a half hours.

• Fraction and a Fraction: This is the most important part of the NCERT solutions for class 7 maths chapter 8 working with fractions. To do this, multiply the top numbers together and the bottom numbers together.

• Rule: Multiply top numbers / Multiply bottom numbers.

• Area Models: Drawing boxes helps you see how much of a shape a fraction takes up. For example, 1/2 of 1/4 means cutting a 1/4 slice into two smaller pieces, which gives you 1/8.

Understanding the Size of the Answer

One common question in NCERT solution for class 7 maths chapter 8 is about the size of the answer after multiplying.

1. Proper Fractions: When you multiply two proper fractions (like 1/2 x 1/3), the answer (1/6) is always smaller than both fractions you started with.

2. Improper Fractions: If you multiply numbers greater than 1, the answer gets bigger.

3. Mixed Numbers: Always turn mixed numbers (like 2 and 1/2) into improper fractions (5/2) before you start multiplying.

Dividing and Turning Fractions Upside Down

Dividing is just multiplying in a different way. This is a common NCERT solutions for class 7 maths chapter 8 working with fractions topic. To master this, you first need to understand the "flip."

1. Reciprocal (The Flip): To find the reciprocal, just flip the fraction upside down. The reciprocal of 3/4 is 4/3. If you multiply a fraction by its flipped version, the answer is always 1. * Example: 5/6 x 6/5 = 30/30 = 1.

2. The Division Step: To divide, keep the first fraction exactly as it is. Change the "divide" sign to a "multiply" sign. Then, flip the second fraction. This is often called "Keep-Change-Flip."

• Example: If 8 badges use 1/2 metre of ribbon, the length for each badge is 1/2 divided by 8. Think of 8 as 8/1. Flip it to 1/8. So, 1/2 x 1/8 = 1/16 metre.

3. Sharing with Friends: If 3 friends share 5 litres of oil, the calculation is 5 divided by 3. Each friend gets 5/3 or 1 and 2/3 litres.

Check Out, Junoon For Class 7 Combo Set of 5 Books

Solving Word Problems: Math in Real Life

Word problems show you how math works in your everyday life. This is a big part of the NCERT solutions for class 7 maths chapter 8.1.

• Cars and Fuel: If a car goes 16 km on 1 litre of gas, how far will it go on 2 and 3/4 litres? First, change 2 and 3/4 to 11/4. Then multiply 16 x 11/4. You can simplify 16 and 4 to get 4 x 11 = 44 km.

• Building a Canal: If a team builds 1 km of a canal in 8 days, they finish 1/8 km in one day. In a 5-day week, they finish 5 x 1/8 = 5/8 km.

• Planting Trees: If you plant 4 saplings in a row with 3/4 metre between each, how long is the row? Remember, there are only 3 gaps between 4 trees! So, 3 x 3/4 = 9/4 or 2 and 1/4 metres.

• Old Indian Math: A very old book called Patiganita by Sridharacharya asks us to add divisions like (1 divided by 1/6) + (1 divided by 1/10). To solve this, we flip the fractions to get 6 + 10, which is 16. This shows how people used fractions a long time ago to solve trade and land problems.

Friendly Advice for Your Math Test

When you solve problems, always show every step. Teachers give points for the way you do the work, even if you make a small mistake in the final answer. Cleaning up your fractions (simplifying) before you multiply will make the work much easier.

Writing Good Answers

Always start by writing down what you already know from the question. This helps you avoid silly mistakes. For example, if Mira reads 1/5 of a 400-page book on Monday and 3/10 on Tuesday, follow these steps:

1. Find pages read on Monday: 1/5 x 400 = 80.

2. Find pages read on Tuesday: 3/10 x 400 = 120.

3. Total read: 80 + 120 = 200.

4. Pages left: 400 - 200 = 200.

Also check, PW School Books

FAQs on Class 7 Maths Chapter 8

1. How do I multiply two fractions?
   Multiply the top numbers together and the bottom numbers together. The answer will be smaller than the fractions you started with if they are proper fractions.

2. What does "reciprocal" mean?
   It means a fraction turned upside down. For example, 2/5 becomes 5/2. Every number except zero has a reciprocal.

3. How do I change a mixed number like 3 and 3/4?
   Multiply the whole number by the bottom (3 x 4 = 12), then add the top 3 to get 15. The improper fraction is 15/4.

4. What does 2/3 of 60 mean?
   In math, "of" means multiply. So, 2/3 x 60 = 120/3 = 40.

5. How do I find the time to fill a tank?
   If 7/10 of a tank fills in 1 hour, the whole tank takes 1 divided by 7/10. Just flip it to get 10/7 or 1 and 3/7 hours.