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.

Last Updated: September 23, 2026

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

Frequently Asked Questions

What number-line concept does this chapter extend?
It extends the basic number line idea beyond simple counting numbers to include concepts like negative numbers and their relative positions, building the foundation needed for later work with integers and rational numbers.

Why is understanding “beyond the point” useful mathematically?
Recognising what lies on either side of a reference point on the number line helps build intuition for comparing values, ordering numbers, and later understanding operations with positive and negative numbers.

Written by Satish

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