NCERT Solutions Ganita Prakash (Part 1) Chapter 1 .5 Patterns in Products — Figure it Out

Book page 141 Updated on2026-09-05

Q1.

Find quick ways to calculate these products: (a) 2 × 1768 × 50 (b) 72 × 125 [Hint: 125 = 1000 ÷ 8] (c) 125 × 40 × 8 × 25

Answer

Regroup the factors so that a 100, 1000 or 10,000 appears.

(a) 2 × 1768 × 50
= (2 × 50) × 1768
= 100 × 1768
= 1,76,800

(b) 72 × 125
= 72 × (1000 ÷ 8)
= (72 ÷ 8) × 1000
= 9 × 1000
= 9,000

(c) 125 × 40 × 8 × 25
= (125 × 8) × (40 × 25)
= 1000 × 1000
= 10,00,000

Why it happens: Multiplication can be done in any order and in any grouping. Spotting the pairs that make round numbers — 2 × 50 = 100, 125 × 8 = 1000, 40 × 25 = 1000 — turns a long multiplication into a one-line answer.

Tip: Useful pairs to memorise: 2 × 5, 4 × 25, 8 × 125, 2 × 50, 20 × 5, 40 × 25.

Q2.

Calculate these products quickly. (a) 25 × 12 = _____ (b) 25 × 240 = _____ (c) 250 × 120 = _____ (d) 2500 × 12 = _____ (e) ______ × ______ = 120000000

Answer

Replace 25 by 100 ÷ 4, 250 by 1000 ÷ 4 and 2500 by 10,000 ÷ 4.

(a) 25 × 12 = (100 ÷ 4) × 12 = 100 × 3 = 300

(b) 25 × 240 = 100 × (240 ÷ 4) = 100 × 60 = 6,000

(c) 250 × 120 = 1000 × (120 ÷ 4) = 1000 × 30 = 30,000

(d) 2500 × 12 = 10,000 × (12 ÷ 4) = 10,000 × 3 = 30,000

(e) 12,00,00,000 can be split in many ways. Three easy ones:

1200 × 1,00,000 = 12,00,00,000
12,000 × 10,000 = 12,00,00,000
1,20,000 × 1,000 = 12,00,00,000

Why it happens: 12,00,00,000 = 12 × 10⁷. Any way of splitting the 12 and the seven zeroes between two factors will work — the zeroes just move from one factor to the other.

Check it yourself: (c) and (d) both give 30,000. Makes sense: 250 × 120 and 2500 × 12 are the same product with a factor of 10 shifted from one number to the other.

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