Page 36 - ICSE Math 6

Example 4: Find the products by suitable rearrangement.
(a) 4 × 167 × 25 (b) 625 × 348 × 16 (c) 125 × 40 × 8 × 25

Solution: (a) 4 × 167 × 25 = (4 × 25) × 167 = 100 × 167 = 16,700
(b) 625 × 348 × 16 = (625 × 16) × 348 = 10,000 × 348 = 34,80,000
(c) 125 × 40 × 8 × 25 = (125 × 8) × (40 × 25) = 1,000 × 1,000 = 10,00,000

Example 5: Find the values of the following.
(a) 297 × 17 + 297 × 3 (b) 38,443 × 94 + 6 × 38,443
(c) 81,265 × 169 – 81,265 × 69

Solution: (a) 297 × 17 + 297 × 3 = 297 × (17 + 3) = 297 × 20 = 5,940
(b) 38,443 × 94 + 6 × 38,443 = 38,443 × 94 + 38,443 × 6 = 38,443 × (94 + 6)
= 38,443 × 100 = 38,44,300
(c) 81,265 × 169 – 81,265 × 69 = 81,265 × (169 – 69) = 81,265 × 100 = 81,26,500

Example 6: Find the products using suitable properties.
(a) 8,431 × 110 (b) 854 × 99 (c) 1,007 × 168

Solution: (a) 8,431 × 110 = 8,431 × (100 + 10) = 8,431 × 100 + 8,431 × 10
= 8,43,100 + 84,310 = 9,27,410

(b) 854 × 99 = 854 × (100 – 1) = 854 × 100 – 854 × 1
= 85,400 – 854 = 84,546
(c) 1,007 × 168 = (1,000 + 7) × (100 + 68)
= 1,000 × 100 + 1,000 × 68 + 7 × 100 + 7 × 68

= 1,00,000 + 68,000 + 700 + 476 = 1,69,176
Example 7: Match the following.
(a) 325 × 130 = 325 × 100 + 325 × 30 (i) Commutativity under multiplication
(b) 3 × 49 × 50 = 3 × 50 × 49 (ii) Commutativity under addition
(c) 80 + 740 + 20 = 80 + 20 + 740 (iii) Distributivity of multiplication over
addition
Solution: (a)-(iii), (b)-(i), (c)-(ii)

Example 8: If the product of two whole numbers is zero, can we say that one or both of them will
be zero? Justify.
Solution: (a) Let’s assume that the two whole numbers ‘a’ and ‘b’ are such that neither ‘a’ nor
‘b’ is zero. The product of any two non-zero whole numbers is a non-zero whole
number. But it is given that a × b = 0, which is not possible. Hence, both ‘a’ and
‘b’ cannot be non-zero.
(b) Let’s assume that any one of the two whole numbers ‘a’ and ‘b’ is zero and the
other is non-zero. Therefore, the product of ‘a’ and ‘b’ would be zero.
(c) Now let’s assume that both the whole numbers ‘a’ and ‘b’ are zeros. Then their
product will also be zero.

Therefore, we can say that if the product of two whole numbers is zero, either one or
both of them are zeros.

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