NCERT Solutions Ganita Prakash (Part 1) Chapter 2 Tinker the Terms II — In-text Questions

Book page 41 Updated on2026-09-05

Q1.
Find this value. (97 × 25 = 100 × 25 – 3 × 25)
Answer
97 × 25 = (100 – 3) × 25
= 100 × 25 – 3 × 25
= 2500 – 75
= 2425
Why it happens: 97 twenty-fives are 100 twenty-fives with 3 twenty-fives taken away. Multiplying by 100 is very easy, and taking away 75 is easy too — much quicker than the usual long multiplication.
Check it yourself: By the usual method, 97 × 25 = 97 × 20 + 97 × 5 = 1940 + 485 = 2425 ✓
Q2.
Use this method to find the following products: (a) 95 × 8 (b) 104 × 15 (c) 49 × 50. Is this quicker than the multiplication procedure you use generally?
Answer
(a) 95 × 8 = (100 – 5) × 8
= 100 × 8 – 5 × 8
= 800 – 40 = 760

(b) 104 × 15 = (100 + 4) × 15
= 100 × 15 + 4 × 15
= 1500 + 60 = 1560

(c) 49 × 50 = (50 – 1) × 50
= 50 × 50 – 1 × 50
= 2500 – 50 = 2450

Yes, it is quicker — each product becomes one easy multiplication by a round number plus one easy addition or subtraction, with no carrying.

Why it happens: This is the distributive property: the multiple of a sum (or difference) is the sum (or difference) of the multiples. Splitting 95 as 100 – 5 keeps the answer the same but makes the arithmetic mental.
Q3.
Which other products might be quicker to find like the ones above?
Answer

Any product where one number sits just above or just below a round number — a multiple of 10, 50, 100 or 1000.

ProductRewrittenValue
98 × 7(100 – 2) × 7 = 700 – 14686
103 × 9(100 + 3) × 9 = 900 + 27927
49 × 5(50 – 1) × 5 = 250 – 5245
52 × 12(50 + 2) × 12 = 600 + 24624
999 × 6(1000 – 1) × 6 = 6000 – 65994
18 × 25(20 – 2) × 25 = 500 – 50450
Why it happens: Multiplying by 10, 100 or 1000 only shifts digits, and 25 or 50 are easy halves and quarters of 100. Splitting the awkward number as round ± small pushes all the difficulty into one tiny product.
Try This: Use it while shopping — 6 packets at ₹99 each is 6 × 100 – 6 = ₹594.
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