Class 7 Mathematics

Chapter 12 Solutions — Another Peek Beyond the Point

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Solutions

Overview

Step-by-step NCERT solutions for Another Peek Beyond the Point (Chapter 12, NCERT Class 7 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Another Peek Beyond the Point textbook chapter.

Solved

What these solutions cover

All 35 questions in Another Peek Beyond the Point are solved in the PDF. Here's what's inside, exercise by exercise:

Decimal Multiplication

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
- (b) 7 × 0.3
- (c) 9 × 5 hundredths
2.
Find the products:
- (a) 27.34 × 6
- (b) 4.23 × 3.7
- (c) 0.432 × 0.23
Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
Meenu bought 4 notebooks and 3 erasers. The cost of each notebook was ₹15.50 and each eraser was ₹2.75. How much did she spend in all?
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 centimeters.
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?
Dwarakanath purchases notebooks at a wholesale price of ₹23.6 per piece and sells each notebook at ₹30/-. How much profit does he make if he sells 50 books in a week?
8.
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?
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
Multiply the following numbers by 10, 100, and 1000 to complete the table: 5.7, 23.02, 0.92, 0.306, 24.67

Decimal Division — Integer Divisor

1.
Find the quotient by converting the denominator into 1, 10, 100, or 1000 and verify the solution by the long division method:
- (a) 18/5
- (b) 415/4
- (c) 1217/2
- (d) 4827/8
2.
Choose the correct answer:
- (a) 1526/4 =
- (i) 38.15
- (ii) 380.15
- (iii) 381.5
- (iv) 381.05
- (b) 3567/8 =
- (i) 4458.75
- (ii) 44.5875
- (iii) 445.875
- (iv) 4458.75
3.
What is the quotient?
- (a) 132 ÷ 4
- (b) 13.2 ÷ 4
- (c) 1.32 ÷ 4
- (d) 0.132 ÷ 4
4.
What is the quotient?
- (a) 126 ÷ 8
- (b) 12.6 ÷ 8
- (c) 1.26 ÷ 8
- (d) 0.126 ÷ 8
- (e) 0.0126 ÷ 8

Decimal Division — Decimal Divisor

1.
Express the following fractions in decimal form:
- (a) 2/5
- (b) 13/4
- (c) 4/50
- (d) 5/8
2.
Find the quotients:
- (a) 24.86 ÷ 1.2
- (b) 5.728 ÷ 1.52
3.
Evaluate the following using the information 156 × 12 = 1872:
- (a) 15.6 × 1.2
- (b) 187.2 ÷ 1.2
- (c) 18.72 ÷ 15.6
- (d) 0.156 × 0.12
4.
Evaluate the following:
- (a) 25 ÷ ____ = 0.025
- (b) 25 ÷ ____ = 250
- (c) 25 ÷ ____ = 2.5
- (d) 25 ÷ 10 = 25 × ____
- (e) 25 ÷ 0.10 = 25 × ____
- (f) 25 ÷ 0.01 = 25 × ____
5.
Find the quotient:
- (a) 2.46 ÷ 1.5
- (b) 2.46 ÷ 0.15
- (c) 2.46 ÷ 0.015 Is the quotient obtained in 24.6 ÷ 1.5 the same as the quotient obtained in 2.46 ÷ 0.15?
A 4 m long wooden block has to be cut into 5 pieces of equal length. What is the length of each piece?
If the perimeter of a regular polygon with 12 sides is 208.8 cm, what is the length of its side?
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.
A car covers 234.45 km using 12.6 litres of petrol. What is the distance travelled per litre?
13.5 kg of flour (aata) was distributed equally among 15 students. How much flour did each student receive?

Look Before You Leap! — Mixed Applications

A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper?
Write the decimal number at the arrow mark: Number line 1: from 3.1 to 3.2, arrow at the 6th division (the tick just right of the tall midpoint tick). Number line 2: from 2.15 to 2.17, arrow at the 6th division (the tick just right of the tall midpoint tick).
Shyamala bought 3 kg bananas at ₹30/- per kg. She counted 35 bananas in all. She sells each banana for ₹5/-. How much profit does she make selling all the bananas?
A teacher placed textbooks that are 2.5 cm thick on a bookshelf. The teacher wanted to place 80 textbooks on the shelf. The bookshelf is 160 cm long. How many books could be placed on the shelf? Was there any space left? If yes, how much?
Fill in the following blanks appropriately: 5.5 km = ___ m, 35 cm = ___ m, 14.5 cm = ___ mm, 68 g = ___ kg, 9.02 m = ___ mm, 125.5 ml = ___ l
The following problem was set by Sridharacharya in his book Patiganita: "6¼ is divided by 2½, and 60¼ is divided by 3½. Tell the quotients separately." Can you try to solve it by converting the fractions into decimals?
7.
Fill the boxes in at least 2 different ways:
- (a) ___ × ___ = 2.4
- (b) ___ × ___ = 14.5
8.
Find the following quotients given that 756 ÷ 36 = 21:
- (a) 75.6 ÷ 3.6
- (b) 7.56 ÷ 0.36
- (c) 756 ÷ 0.36
- (d) 75.6 ÷ 360
- (e) 7560 ÷ 3.6
- (f) 7.56 ÷ 0.36
Find the missing cells if each cell represents a ÷ b. b \ a → 1517 151.7 15.17 1.517 15170 37 : 41 ___ ___ ___ ___ 3.7: ___ 41 4.1 ___ ___ 0.37: ___ ___ 41 ___ ___ 0.037: ___ 4100 ___ 41 ___ 370: ___ ___ ___ ___ 41
10.
Using the digits 2, 4, 5, 8, and 0 fill the boxes __ __ . __ × __ . __ to get the:
- (a) maximum product
- (b) minimum product
- (c) product greater than 150
- (d) product nearest to 100
- (e) product nearest to 5
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

Sample

Worked examples

3 questions from Another Peek Beyond the Point, solved step by step.

Decimal Multiplication

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 centimeters.

Total height = 1.45 × 36 mm

145 × 36 = 5220

Digits after decimal: 2 + 0 = 2

1.45 × 36 = 52.20 mm

Convert to cm: 52.20 mm ÷ 10 = 5.22 cm

Answer: Total height = 5.22 cm

Decimal Division — Decimal Divisor

Find the quotients: (a) 24.86 ÷ 1.2 (b) 5.728 ÷ 1.52

(a) 24.86 ÷ 1.2:

Multiply both by 10: 248.6 ÷ 12 = 2486 ÷ 120 = 1243/60

1243/60 = 20.716... (non-terminating, repeating)

24.86 ÷ 1.2 ≈ 20.72 (to 2 decimal places)

(b) 5.728 ÷ 1.52:

Multiply both by 100: 572.8 ÷ 152 = 5728 ÷ 1520 = 358/95

358/95 = 3.768... (non-terminating, repeating)

5.728 ÷ 1.52 ≈ 3.77 (to 2 decimal places)

Answer: (a) 24.86 ÷ 1.2 ≈ 20.72 (b) 5.728 ÷ 1.52 ≈ 3.77

Look Before You Leap! — Mixed Applications

A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper?

Price per gram of peanut chikki = 70.5 ÷ 210

= 705/2100 = 47/140 ≈ ₹0.3357 per gram

Price per gram of potato chips = 33.25 ÷ 110

= 3325/11000 = 133/440 ≈ ₹0.3023 per gram

0.3023 < 0.3357, so potato chips are cheaper per gram.

Answer: Potato chips (≈ ₹0.30/g) are cheaper than peanut chikki (≈ ₹0.34/g).

All 35 questions in Another Peek Beyond the Point are solved step by step in the Solutions PDF above.

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Chapter 12 Solutions — Another Peek Beyond the Point

Overview

What these solutions cover

Decimal Multiplication

Decimal Division — Integer Divisor

Decimal Division — Decimal Divisor

Look Before You Leap! — Mixed Applications

Worked examples

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 centimeters.

Find the quotients: (a) 24.86 ÷ 1.2 (b) 5.728 ÷ 1.52

A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper?

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