NCERT Solutions for Class 7 Maths Chapter 12: Another Peek Beyond the Point – Ganita Prakash Part 2

Complete NCERT Solutions for Class 7 Maths Chapter 12 “Another Peek Beyond the Point” from the Ganita Prakash Part 2 textbook, covering decimal multiplication, decimal division, division with a decimal divisor, and real-life applications with step-by-step working. These Class 7 Mathematics Chapter 12 solutions are also useful as quick revision notes before exams.

Multiplying Decimal Numbers (Figure It Out – Page 73)

Rule: multiply the numbers as if they were whole numbers, then count the total number of digits after the decimal point in both factors together — the product has that many decimal digits.

Finding products:

• 27.34 × 6: 2734 × 6 = 16404, with 2 decimal digits from 27.34 and 0 from 6 → 164.04
• 4.23 × 3.7: 423 × 37 = 15651, with 2+1 = 3 decimal digits → 15.651
• 0.432 × 0.23: 432 × 23 = 9936, with 3+2 = 5 decimal digits → 0.09936

Cloth for curtains: 3 pieces of cloth, each 1.65 m long — total length = 1.65 × 3 = 4.95 m.

Shopping bill: 4 notebooks at ₹15.50 each and 3 pens at ₹2.75 each — total = (4 × 15.50) + (3 × 2.75) = 62.00 + 8.25 = ₹70.25.

Stack of coins: each coin is 1.45 mm thick; a stack of 36 coins — height = 1.45 × 36 = 52.2 mm = 5.22 cm.

Buying oranges: oranges cost ₹56.50 per kg; 2.250 kg bought — cost = 56.50 × 2.250 = ₹127.125, about ₹127.13.

Selling milk at a profit: 50 litres sold at a profit of ₹6.40 per litre — total profit = 50 × 6.40 = ₹320.

Patterns in Decimal Products (using 18 × 12 = 216)

Once 18 × 12 = 216 is known, related decimal products can be found just by counting decimal places, without fresh multiplication:

• 18 × 1.2 = 21.6
• 18 × 0.12 = 2.16
• 1.8 × 1.2 = 2.16
• 0.18 × 0.12 = 0.0216
• 0.018 × 0.012 = 0.000216
• 1.8 × 12 = 21.6

Why the product changes size: if both factors are greater than 1, the product exceeds both; if both factors are between 0 and 1, the product is smaller than both; if one factor is between 0 and 1 and the other is greater than 1, the product lies between the two factors.

Dividing Decimal Numbers (Figure It Out – Page 83)

Converting fractions to decimals (write the denominator as a power of 10, or use long division):

• 18/5 = 36/10 = 3.6
• 415/4 = 10375/100 = 103.75
• 1217/2 = 6085/10 = 608.5
• 4827/8 = 603375/1000 = 603.375

Shifting the decimal point in the quotient: once 132 ÷ 4 = 33 is known, moving the decimal point in the dividend moves it the same way in the quotient:

• 132 ÷ 4 = 33
• 13.2 ÷ 4 = 3.3
• 1.32 ÷ 4 = 0.33
• 0.132 ÷ 4 = 0.033

Effect of a decimal divisor on the quotient (dividend fixed at 2.46):

• 2.46 ÷ 1.5 = 1.64
• 2.46 ÷ 0.15 = 16.4 (divisor 10 times smaller → quotient 10 times bigger)
• 2.46 ÷ 0.015 = 164 (divisor 100 times smaller than 1.5 → quotient 100 times bigger)

Division with a Decimal Divisor (Figure It Out – Page 86–87)

Method: multiply both the dividend and the divisor by the same power of 10 so the divisor becomes a whole number, then divide as usual — the quotient does not change. For example, 48.65 ÷ 3.5 becomes 486.5 ÷ 35 (both multiplied by 10) = 13.9.

Long-division quotients:

• 24.86 ÷ 1.2 → 248.6 ÷ 12 = 20.71… (a non-terminating quotient)
• 5.728 ÷ 1.52 → 572.8 ÷ 152 = 3.76… (a non-terminating quotient)

Sharing a wooden plank: a 4 m plank cut into 5 equal pieces — each piece = 4 ÷ 5 = 0.8 m.

Regular polygon perimeter: a 12-sided regular polygon has perimeter 208.8 cm — each side = 208.8 ÷ 12 = 17.4 cm.

Sharing juice: 3 litres of juice shared equally among 8 people — each share = 3 ÷ 8 = 0.375 litres = 375 mL.

Fuel efficiency: a vehicle covers 234.45 km using 12.6 litres of petrol — efficiency = 234.45 ÷ 12.6 ≈ 18.61 km/litre.

Dividing flour: 13.5 kg of flour divided equally into 15 packets — each packet = 13.5 ÷ 15 = 0.9 kg.

Look Before You Leap – Real-Life Applications (Pages 93–95)

Comparing prices per gram: potato chips work out to about ₹0.30 per gram and peanut chikki to about ₹0.34 per gram — comparing the unit rate directly (not just the pack price) shows which snack is cheaper per gram, even when pack sizes differ.

Combining profit and loss: a vendor earns a profit of ₹5 on each of 35 units sold, but also has to write off 3 spoiled units worth ₹30 each — net profit = (35 × 5) − (3 × 30) = 175 − 90 = ₹85.

Bookshelf capacity: a 160 cm shelf holds books that are each 2.5 cm thick — number of books = 160 ÷ 2.5 = 64 books, fitting exactly with no space left over.

Practice more: Extra Questions for Class 7 Maths Chapter 12

Quick revision: Revision Notes for Class 7 Maths Chapter 12

See the full book: NCERT Books for Class 7 Maths Part 2

Written by Satish

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