Q: By what number should we multiply Patna’s population to get a number/population close to that of Mumbai?

Mumbai’s population by Patna’s population in 2011 = $\frac{1,24,42,373}{16,84,222}$ ~ 7 Patna’s population needs to be multiplied by 7 to be close to Mumbai’s population. 1.5 Patterns in Products A Multiplication Shortcut NCERT In-Text Questions (Page 14) Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10? Solution: We know that 5 × 2 = 10 (multiplication fact) has two division facts: 10 ÷ 2 = 5 and 10 ÷ 5 = 2. So, according to the question, we can use $\frac{10}{2}$ in place of 5. Either we 10 divide by 5 or by $\frac{10}{2}$, we will get the same answer. Figure it Out (Page 14)

Q: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several oceans. Albatrosses can cover about 900-1000 km in a day. One of the longest single trips recorded is about 12,000 km. How many days would such a trip take to cross the Pacific Ocean approximately?

Using 900 km/day: $\frac{12000}{900}$ km ~ 13 days So, it would take about 13 days. Using 1000 km/day: $\frac{12000}{1000}$ km = 12 days So, it would take about 12 days. It would take approximately 12-13 days to complete the 12,ooo km trip.

Question 1

According to the 2011 Census, the population of the town of Chintamani was about 75,000. How much less than one lakh is 75,000?

Accepted Answer

One lakh = 1,00,000
Now, 1,00,000 – 75,000 = 25,000
Thus, the population of Chintamani in 2011 was 25,000 less than one lakh.

Source: This question is from Large Numbers Around Us, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Large Numbers Around Us: According, Census, Population, Town, Chintamani, Less. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Large Numbers Around UsQ10: You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get...
Q11: Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each...
Q12: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several...
Q13: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560...
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Question 2

The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?

Accepted Answer

1,06,000 – 1,00,000 = 6,000
Thus, the population in 2024 is 6,000 more than one lakh.

Source: This question is from Large Numbers Around Us, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Large Numbers Around Us: Estimated, Population, Chintamani, Year, Lakh, Large Numbers Around Us. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Large Numbers Around UsQ10: You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get...
Q11: Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each...
Q12: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several...
Q13: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560...
Q14: Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is...
Practice more questions from Large Numbers Around Us &mdash; Mathematics, Class 7 CBSE

Question 3

By how much did the population of Chintamani increase from 2011 to 2024?

Accepted Answer

The population increase from 2011 to 2024 = 1,06,000 – 75,000 = 31,000
Getting a Feel of Large Numbers
You may have come across interesting facts like these:
• The world’s tallest statue is the ‘Statue of Unity’ in Gujarat depicting Sardar Vallabhbhai Patel. Its height is about 180 metres.
• Kunchikal waterfall in Karnataka is said to drop from a height of about 450 metres.
It is not always easy to get a sense of how big these measurements are. But, we can get a better sense of their size when we compare them with something familiar. Let us see an example.
NCERT In-Text Questions (Page 3)
Look at the picture on the right. Somu is 1 metre tall. If each floor is about four times his height, what is the approximate height of the building?
Solution:
Somu’s height = 1 m
Height of a floor = 4 × Somu’s height
= 4 × 1 m
= 4 m
Approximate height of the building = Height of 11 floors
= 11 × 4 m
= 44 m
Which is taller — The Statue of Unity or this building? How much taller?
__________ m
Solution:
The Statue of Unity is 180 m tall, and the building is 44 m tall.
Difference in heights = 180 – 44 = 136 m.
The Statue of Unity is taller than the building.
How much taller is the Kunchikal waterfall than Somu’s building?
__________ m
Solution:
Kunchikal waterfall is 450 m tall, and the building is 40 m tall.
Difference in heights = 450 – 44 = 406 m
Thus, the Kunchikal waterfall is 406 m taller than the building.
How many floors should Somu’s building have to be as high as the waterfall?
__________
Solution:
Each floor is 4 m tall. To match the height of the waterfall (450 m), floors needed = 450 ÷ 4 = 112.5.
Thus, building would need approximately 113 floors to be as high as the waterfall.
Is One Lakh a Very Large Number?
NCERT In-Text Questions (Page 4)
How do you view a lakh — is a lakh big or small?
Solution:
One lakh is a big number in terms of counting numbers.
Reading and Writing Numbers
NCERT In-Text Questions (Pages 4-5)
Write each of the numbers given below in words:
(a) 3,00,600
(b) 5,04,085
(c) 27,30,000
(d) 70,53,138
Solution:
(a) 3,00,600 → Three lakh six hundred
(b) 5,04,085 → Five lakh four thousand eighty-five
(c) 27,30,000 → Twenty-seven lakh thirty thousand
(d) 70,53,138 → Seventy lakh fifty-three thousand one hundred thirty-eight
Write the corresponding number in the Indian place value system for each of the following:
(a) One lakh twenty-three thousand four hundred fifty-six
(b) Four lakh seven thousand seven hundred four
(c) Fifty lakh five thousand fifty
(d) Ten lakh two hundred thirty-five
Solution:
(a) 1,23,456
(b) 4,07,704
(c) 50,05,050
(d) 10,00,235
1.2 Land of Tens
NCERT In-Text Questions (Pages 5-6)

Question 4

Which city’s population increased the most between 2001 and 2011?

Accepted Answer

Bengaluru experienced the largest population increase, with a growth of 41,24,644 people.

Source: This question is from Large Numbers Around Us, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Large Numbers Around Us: City, Population, Increased, Large Numbers Around Us, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Large Numbers Around UsQ10: You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get...
Q11: Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each...
Q12: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several...
Q13: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560...
Q14: Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is...
Practice more questions from Large Numbers Around Us &mdash; Mathematics, Class 7 CBSE

Question 5

Two of the many different ways to get 5072 are shown below:
These two ways can be expressed as:
(a) (50 × 100) + (7 × 10) + (2 × 1) = 5072
(b) (3 × 1000) + (20 × 100) + (72 × 1) = 5072
Find a different way to get 5072 and write an expression for the same.

Accepted Answer

5 × 1000 + 7 × 10 + 2 × 1
Figure it Out (Pages 6-7)
For each number given below, write expressions for at least two different ways to obtain the number through button clicks. Think like Chitti and be creative.
(а) 8300
(b) 40629
(c) 56354
(d) 66666
(e) 367813
Solution:
(a) (i) (8 × 1000) + (3 × 100) = 8300
(ii) (83 × 100) = 8300
(b) (i) (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1) = 40629
(ii) (40 × 1000) + (6 × 100) + (29 × 1) = 40629
(c) (i) (5 × 10000) + (6 × 1000) + (3 × 100) + (54 × 1) = 56354
(ii) (56 × 1000) + (35 × 10) + (4 × 1) = 56354
(d) (i) (6 × 10000) + (6 × 1000) + (6 × 100) + (66 × 1) = 66666
(ii) (66 × 1000) + (66 × 10) + (6 × 1) = 66666
(e) (i) (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100)+ (13 × 1) = 367813
(ii) (36 × 10000) + (7813 × 1) = 367813
NCERT In-Text Questions (Page 7)
Creative Chitti has some questions for you-
(a) You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make?
(b) 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?
Solution:
(a) For the largest 3-digit number:
Press the +100 button 9 times: 9 × 100 = 900
Add 10 more presses using the +10 button: 10 × 10 = 100
Add the remaining 11 presses using the +1 button: 11 × 1 = 11
Sum: 900 + 100 + 11 = 1011, but that’s a 4-digit number.
Scale back by reducing the number of +10 presses to 8 and +1 presses to 13.
Largest 3-digit number: 993 (9 × 100 + 8 × 10 + 13 × 1)
For the smallest 3-digit number
Press the +10 button 8 times: 8 × 10 = 80
Add 22 more presses using the +1 button: 22 × 1 = 22
Smallest 3-digit number: 102 (8 × 10 + 22 × 1)
(b) 997 with 34 Clicks
9 × (+100) = 900
8 × (+10) = 80
17 × (+1) = 17
Create questions like these and challenge your classmates.
Solution:
Do it yourself.
Systematic Sippy is a different kind of calculator. It has the following buttons:
+1, +10, +100, +1000, +10000, +100000.
It wants to be used as minimally as possible.
How can we get the numbers (a) 5072, (b) 8300 using as few button clicks as possible?
Find out which buttons should be clicked and how many times to get the desired numbers given in the table. The aim is to click as few buttons as possible.
Here is one way to get the number 5072. This method uses 23 button clicks in total.
Is there another way to get 5072 using fewer than 23 button clicks?
Write the expression for the same.
Solution:
(a) 5 × (+1000) = 5000 (5 clicks)
7 × (+10) = 70 (7 clicks)
2 × (+1) = 2 (2 clicks)
Total clicks: 5 + 7 + 2 = 14 clicks
Expression: 5 × 1000 + 7 × 10 + 2 × 1 = 5072
(b)
For 8300: 8 × (+1000) = 8000
For: 3 × (+100) = 300
Total = 8000 + 300 = 8300
Figure it Out (Page 7)

Question 6

By what number should we multiply Patna’s population to get a number/population close to that of Mumbai?

Accepted Answer

Mumbai’s population by Patna’s population in 2011 = $\frac{1,24,42,373}{16,84,222}$ ~ 7
Patna’s population needs to be multiplied by 7 to be close to Mumbai’s population.
1.5 Patterns in Products
A Multiplication Shortcut
NCERT In-Text Questions (Page 14)
Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10?
Solution:
We know that 5 × 2 = 10 (multiplication fact) has two division facts: 10 ÷ 2 = 5 and 10 ÷ 5 = 2.
So, according to the question, we can use $\frac{10}{2}$ in place of 5. Either we 10
divide by 5 or by $\frac{10}{2}$, we will get the same answer.
Figure it Out (Page 14)

Question 7

A calculator has only ‘+10,000’ and ‘+100’ buttons. Write an expression describing the number of button clicks to be made for the following numbers:
(a) 20,800
(b) 92,100
(c) 1,20,500
(d) 65,30,000
(e) 70,25,700

Accepted Answer

(a) 20,800 = 2 × 10,000 + 8 × 100
Number of clicks = 2 + 8 = 10 clicks
(b) 92,100 = 9 × 10,000 + 21 × 100
Number of clicks = 9 + 21 = 30 clicks
(c) 1,20,500 = 12 × 10,000 + 5 × 100
Number of clicks = 12 + 5 = 17 clicks
(d) 65,30,000 = 653 × 10,000 + 0 × 100
Number of clicks = 653 + 0 = 653 clicks
(e) 70,25,700 = 702 × 10,000 + 57 × 100
Number of clicks = 702 + 57 = 759 clicks

Question 8

How many lakhs make a billion?

Accepted Answer

1 lakh = 1,00,000
1 billion = 1,000,000,000
So, 1,000,000,000 ÷ 1,00,000 = 10,000.
Thus, 10,000 lakhs make a billion.

Source: This question is from Large Numbers Around Us, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Large Numbers Around Us: Lakhs, Make, Billion, Large Numbers Around Us, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Large Numbers Around UsQ10: You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get...
Q11: Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each...
Q12: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several...
Q13: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560...
Q14: Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is...
Practice more questions from Large Numbers Around Us &mdash; Mathematics, Class 7 CBSE

Question 9

You are given two sets of number cards numbered from 1-9. Place a number card in each box below to get the (a) largest possible sum, (b) smallest possible difference of the two resulting numbers.

Accepted Answer

(a) Largest possible sum = 9988776 + 65544 = 10054320
(b) Smallest possible difference = 1122334 – 99887 = 1022447

Source: This question is from Large Numbers Around Us, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Large Numbers Around Us: Sets, Number, Cards, Numbered, Place, Card. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Large Numbers Around UsQ10: You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get...
Q11: Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each...
Q12: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several...
Q13: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560...
Q14: Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is...
Practice more questions from Large Numbers Around Us &mdash; Mathematics, Class 7 CBSE

Question 10

You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get as close as you can to the numbers below using any operation you want. Each card can be used only once to make a particular number.
(a) 1,10,000: Closest I could make is 4000 × (20 + 5) + 13000 = 1,13,000
(b) 2,00,000:
(c) 5,80,000:
(d) 12,45,000:
(e) 20,90,800:

Accepted Answer

(a) 4000 × (20 + 5) + 13000
= 4000 × 25 + 13000
= 100000+ 13000
= 113000
This gives us 1,13,000, which is very close to 1,10,000.
(b) 1,50,000 + 70,000 – 4000 × 5 = 2,00,000
(c) 70,000 × 5 + 1,50,000 + 4,000 × 20 = 5,80,000
(d) 70,000 × 20 – 1,50,000 – 4,000 – 300 × 5 = 12,44,500
This gives us 12,44,500, which is very close to 12,45,000.
(e) 13,000 × 300 – 70,000(20 + 5) – 1,50,000 + 4,000 = 20,04,000

Question 11

Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is 1 mm thick.

Accepted Answer

The approximate height of the Statue of Unity is 180 m (1,80,000 mm)
Thickness of one coin = 1 mm [Given]
To match the height, we need: 1,82,000 coins

Source: This question is from Large Numbers Around Us, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Large Numbers Around Us: Out, Coins, Stacked, Match, Height, Statue. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Large Numbers Around UsQ10: You are given some number cards: 4000, 13000, 300, 70000, 150000, 20, and 5. Using the cards, get...
Q12: Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several...
Q13: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560...
Q14: Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is...
Q2: The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is...
Practice more questions from Large Numbers Around Us &mdash; Mathematics, Class 7 CBSE

Question 12

Grey-headed albatrosses have a roughly 7-foot wingspan. They are known to migrate across several oceans. Albatrosses can cover about 900-1000 km in a day. One of the longest single trips recorded is about 12,000 km. How many days would such a trip take to cross the Pacific Ocean approximately?

Accepted Answer

Using 900 km/day:
$\frac{12000}{900}$ km ~ 13 days
So, it would take about 13 days.
Using 1000 km/day:
$\frac{12000}{1000}$ km = 12 days
So, it would take about 12 days.
It would take approximately 12-13 days to complete the 12,ooo km trip.

Question 13

A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560 km from Alaska to Australia without stopping. Its journey started on 13 October 2022 and continued for about 11 days. Find out the approximate distance it covered every day. Find out the approximate distance it covered every hour.

Accepted Answer

Total distance = 13,560 km and duration = 11 days
Distance covered every day = 13,560 ÷ 11 ~ 1,233 km/day.
Thus, the godwit covers approximately 1,233 km per day.
One day = 24 hours
Distance covered every hour = 1,233 ÷ 24 ~ 51 km/hour.
Thus, the godwit covers approximately 51 km per hour.

Question 14

Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is about 8850 m high. Aeroplanes can fly as high as 10,000 – 12,800 m. How many times bigger are these heights compared to Somu’s building?

Accepted Answer

Let’s compare these heights to Somu’s building:
Bald eagle: 4500 – 6000 m;
Mount Everest: 8850 m;
Aeroplanes: 10,000 – 12,800 m
Somu’s building is 44 m tall.
Ratios compared to Somu’s building:
Bald eagle: (4500 ÷ 44 ~ 100) to (6000 ÷ 44 ~ 150)
The bald eagle’s flying height is 100 – 150 times higher.
Mount Everest: 8850 ÷ 44 = 201
Mount Everest is 201 times bigger.
Aeroplanes: (10,000 ÷ 44 ~ 230) to (12,800 ÷ 44 ~ 290)
An aeroplane’s flying height is 230 – 290 times higher.