Page 39 - Start Up Mathematics_6

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 8: 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 9: A bus driver filled the bus tank with 33 L of diesel. Two days later he filled the tank
with 17 L of diesel. If the diesel costs ` 28 per litre, how much did he spend in all
on diesel?
Solution: Diesel filled on first day = 33 L
Diesel filled two days later = 17 L
Cost of diesel = ` 28 per litre

Total expenditure on fuel = 33 × 28 + 17 × 28
= (33 + 17) × 28 = 50 × 28 = ` 1,400
Example 10: Match the following:

(a) 325 × 136 = 325 × (6 + 30 + 100) (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 11: If the product of two whole numbers is zero, can we say that one or both of them
will be zero? Justify. (NCERT)
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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