Q: Given that 18 × 12 = 216, find the products: (a) 18 × 1.2 (b) 18 × 0.12 (c) 1.8 × 1.2 (d) 0.18 × 0.12 (e) 0.018 × 0.012 (f) 1.8 × 12 In which of the cases above is the product less than 1?

(a) Here 18 × 12 = 216 …..(i) Now 18 × 1.2 = $\frac{18 \times 12}{10}$ [Using (i)] = $\frac {216}{10}$ = 21.6 (1 decimal place) (b) 18 × 0.12 = $\frac{18 \times 12}{100}$ (Using (i)) = $\frac {216}{100}$ = 2.16 (2 decimal places) (c) 1.8 × 1.2 = $\frac{18}{10} \times \frac{12}{10}=\frac{216}{100}$ [Using (i)] = 2.16 (2 decimal places) (d) 0.18 × 0.12 = $\frac{18}{100} \times \frac{12}{100}=\frac{216}{100 \times 100}$ [Using (i)] = 0.0216 (4 decimal places) (e) 1.8 × 12 = $\frac{18 \times 12}{10}=\frac{216}{10}$ [Using (i)] = 21.6 (1 decimal place) When multiplying two numbers positive if both numbers are less than 1, their product will also be less than 1. In (d) and (e) product is less than 1.

Question 1

Recall that a tenth is 0.1, a hundredth is 0.01, and so on. Find the following products in tenths, hundredths, and so on:
(a) 6 × 4 tenths = 24 tenths
(b) 7 × 0.3
(c) 9 × 5 hundredths

Accepted Answer

(a) Here, 6 × 4 tenths = 24 tenths.
(b) 7 × 0.3 = 7 × 3 tenths = 21 tenths
(c) Here, 9 × 5 hundredths = 45 hundredths

Source: This question is from Another Peek Beyond the Point, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Another Peek Beyond the Point: Recall, Tenth, Hundredth, Products, Tenths, Hundredths. 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 Another Peek Beyond the PointQ10: Multiplying the following numbers by 10, 100, and 1000 to complete the table.
Q11: Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c)...
Q2: Choose the correct answer: (a) $\frac {1526}{4}$ = _____ (i) 38.15 (ii) 380.15 (iii) 381.5 (iv)...
Q3: Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
Q4: Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹ 15.50, and each eraser was ₹...
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Question 2

Choose the correct answer:
(a) $\frac {1526}{4}$ = _____
(i) 38.15
(ii) 380.15
(iii) 381.5
(iv) 381.05
(b) $\frac {3567}{8}$ = _____
(i) 4458.75
(ii) 44.5875
(iii) 445.875
(iv) 4458.75

Accepted Answer

(a) $\frac {1526}{4}$
By using the Long Division Method:
Hence, option (iii) is correct.
(b) Given $\frac {3567}{8}$
By using the Long Division Method:
Hence, option (iii) is correct.

Source: This question is from Another Peek Beyond the Point, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Another Peek Beyond the Point: Choose, Correct, Frac, Iii, Another Peek Beyond the Point, 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 Another Peek Beyond the PointQ10: Multiplying the following numbers by 10, 100, and 1000 to complete the table.
Q11: Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c)...
Q3: Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
Q4: Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹ 15.50, and each eraser was ₹...
Q5: The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by...
Practice more questions from Another Peek Beyond the Point &mdash; Mathematics, Class 7 CBSE

Question 3

Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?

Accepted Answer

Given: Thejus needs 1.65 m of cloth for a shirt.
For 3 shirts, the total cloth needed = 1.65 × 3
= $\frac {165}{100}$ × 3
= $\frac {495}{100}$
= 4.95

Source: This question is from Another Peek Beyond the Point, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Another Peek Beyond the Point: Thejus, Needs, Cloth, Shirt, Metres, Needed. 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 Another Peek Beyond the PointQ10: Multiplying the following numbers by 10, 100, and 1000 to complete the table.
Q11: Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c)...
Q2: Choose the correct answer: (a) $\frac {1526}{4}$ = _____ (i) 38.15 (ii) 380.15 (iii) 381.5 (iv)...
Q4: Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹ 15.50, and each eraser was ₹...
Q5: The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by...
Practice more questions from Another Peek Beyond the Point &mdash; Mathematics, Class 7 CBSE

Question 4

Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹ 15.50, and each eraser was ₹ 2.75. How much did she spend in all?

Accepted Answer

Here cost of 1 notebook = ₹ 15.50
∴ Cost of 4 notebooks = 4 × 15.50
= $\frac{4 \times 1550}{100}$
= $\frac {6200}{100}$
= ₹ 62
and cost of 1 eraser = ₹ 2.75
∴ Cost of 3 erasers = 3 × ₹ 2.75
= $\frac{3 \times 275}{100}$
= $\frac {825}{100}$
= ₹ 8.25
∴ Total amount spent = 62 + 8.25 = ₹ 70.25

Question 5

The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by placing 36 rupee coins one over the other? Write the answer in centimetres.

Accepted Answer

Thickness of 1 coin = 1.45 mm
Total thickness of 36 coins = 36 × 1.45
= $\frac{36 \times 145}{100}$
= $\frac {5220}{100}$
= 52.2 mm
Now 10 mm = 1 cm
1 mm = $\frac {1}{10}$ cm
∴ 52.2 mm = $\frac {52.2}{10}$ = 5.22 cm.

Question 6

The price of 1 kg of oranges is ₹ 56.50. What is the price of 2.250 kg of oranges? Can we write 56.50 as 56.5 and 2.250 as 2.25 and multiply? Will we get the same product? Why?

Accepted Answer

Price of 1 kg of oranges = ₹ 56.50
Price of 2.250 kg of oranges = 56.50 × 2.250
= $\frac{5650 \times 2250}{100 \times 1000}$
= $\frac {12712500}{100000}$
= ₹ 127.125
Now 56.5 × 2.25 = 127.125
Hence, we will get the same product.
The zeroes at the end of a decimal do not change its value.
As we saw, 56.50 is the same as 56.5, and 2.250 is the same as 2.25.
Hence, the product of the two numbers will be the same.

Question 7

Given that 18 × 12 = 216, find the products:
(a) 18 × 1.2
(b) 18 × 0.12
(c) 1.8 × 1.2
(d) 0.18 × 0.12
(e) 0.018 × 0.012
(f) 1.8 × 12
In which of the cases above is the product less than 1?

Accepted Answer

(a) Here 18 × 12 = 216 …..(i)
Now 18 × 1.2 = $\frac{18 \times 12}{10}$ [Using (i)]
= $\frac {216}{10}$
= 21.6 (1 decimal place)
(b) 18 × 0.12 = $\frac{18 \times 12}{100}$ (Using (i))
= $\frac {216}{100}$
= 2.16 (2 decimal places)
(c) 1.8 × 1.2 = $\frac{18}{10} \times \frac{12}{10}=\frac{216}{100}$ [Using (i)]
= 2.16 (2 decimal places)
(d) 0.18 × 0.12 = $\frac{18}{100} \times \frac{12}{100}=\frac{216}{100 \times 100}$ [Using (i)]
= 0.0216 (4 decimal places)
(e) 1.8 × 12 = $\frac{18 \times 12}{10}=\frac{216}{10}$ [Using (i)]
= 21.6 (1 decimal place)
When multiplying two numbers positive if both numbers are less than 1, their product will also be less than 1.
In (d) and (e) product is less than 1.

Question 8

3 litres of watermelon juice is shared among 8 friends equally. How much watermelon juice will each get? Express the quantity of juice in millilitres.

Accepted Answer

Here total quantity of juice = 3 litres
No. of friends = 8
∴ Juice per friend = $\frac {3}{8}$ litre
= $\frac {3}{8}$ × 1000 ml
= $\frac {3000}{8}$
= 375 ml

Source: This question is from Another Peek Beyond the Point, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Another Peek Beyond the Point: Litres, Watermelon, Juice, Shared, Friends, Equally. 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 Another Peek Beyond the PointQ10: Multiplying the following numbers by 10, 100, and 1000 to complete the table.
Q11: Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c)...
Q2: Choose the correct answer: (a) $\frac {1526}{4}$ = _____ (i) 38.15 (ii) 380.15 (iii) 381.5 (iv)...
Q3: Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
Q4: Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹ 15.50, and each eraser was ₹...
Practice more questions from Another Peek Beyond the Point &mdash; Mathematics, Class 7 CBSE

Question 9

In which of the following multiplications is the product less than 1? Can you find the answer without actually doing the multiplications?
(a) 7 × 0.6
(b) 0.7 × 0.6
(c) 0.7 × 6
(d) 0.07 × 0.06

Accepted Answer

Yes, we can find the answer without actual multiplication, only by using decimal place values.
Multiplying by a number greater than 1: The product is greater than the original number.
Multiplying by a number between 0 and 1: The product is less than the original number.
Multiplying two numbers between 0 and 1: The product will be less than both factors, and therefore definitely less than 1.
(a) Greater than 1.
(b) Less than 1.
(c) Greater than 1.
(d) Less than 1.

Question 10

Multiplying the following numbers by 10, 100, and 1000 to complete the table.

Accepted Answer

4.3 Decimal Division
Figure It Out (Page 83)

Source: This question is from Another Peek Beyond the Point, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Another Peek Beyond the Point: Multiplying, Numbers, Complete, Table, Another Peek Beyond the Point, 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 Another Peek Beyond the PointQ11: Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c)...
Q2: Choose the correct answer: (a) $\frac {1526}{4}$ = _____ (i) 38.15 (ii) 380.15 (iii) 381.5 (iv)...
Q3: Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
Q4: Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹ 15.50, and each eraser was ₹...
Q5: The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by...
Practice more questions from Another Peek Beyond the Point &mdash; Mathematics, Class 7 CBSE

Question 11

Sort the following expressions in increasing order:
(a) 245.05 × 0.942368
(b) 245.05 × 7.9682
(c) 245.05 ÷ 7.9682
(d) 245.05 ÷ 0.942368
(e) 245.05
(f) 7.9682

Accepted Answer

Let A = 245.05, B = 0.942368, C = 7.9682
We note that B  1
(a) Now A × B = 245.05 × 0.942368  245.05
(Multiplying a number by a value greater than 1 results in a larger number)
(c) A ÷ C = 2.4505 ÷ 7.9682  245.05
(Dividing a number by a value greater than 1 results in a larger number)
(e) Now, expression less than 245.05
∴ 0.942368 is closer to 1 than 7.9682 is to 1.
0.942368 will result in a value closer to 245.05 than dividing by 7.9682.
∴ (c)