Page 17 - Start Up Mathematics_7

Example 14: Verify that 9 × {7 + (–3)} = {9 × 7} + {9 × (–3)}.

Solution: 9 × {7 + (–3)} = {9 × 7} + {9 × (–3)}
LHS = 9 × {7 + (–3)} = 9 × {7 – 3} = 9 × 4 = 36

RHS = {9 × 7} + {9 × (–3)} = 63 + (–27) = 63 – 27 = 36
 LHS = RHS, hence verified.
Example 15: (a) For any integer n, what is (–1) × n equal to?

(b) Determine the integer whose product with (–1) is:
(i) –21 (ii) 31 (iii) 0

Solution: (a) For any integer n, (–1) × n = –n.
(b) Integer whose product with (–1) is:

(i) –21 is 21 (ii) 31 is –31 (iii) 0 is 0
Example 16: Find the value of the expression (|–12| + |2 – 26|) × |13 – 25|
Solution: (|–12| + |2 – 26|) × |13 – 25| = (12 + |–24|) × |–12|

= (12 + 24) × 12
= 36 × 12 = 432

Example 17: Evaluate the following using suitable properties. Also mention the properties used.
(a) (275 × 163) × 0 (b) 325 × (–23) + 325 × 23
Solution: (a) (275 × 163) × 0 = 275 × (163 × 0) (Associative property)

= 275 × 0 = 0
(b) 325 × (–23) + 325 × 23 = 325 × (–23 + 23) (Distributive property)

= 325 × 0 = 0
Example 18: Find the product using suitable properties:
(a) 26 × (–37) + (–37) × 74 (b) 8 × 47 × (–125)

(c) (–17) × 102 (d) (–625) × (–47) + (–625) × (–53)
Solution: (a) 26 × (–37) + (–37) × 74 = (–37) × 26 + (–37) × 74 (Commutative property)

= (–37) × (26 + 74) (Distributive property)
= (–37) × 100 = –3,700
(b) 8 × 47 × (–125) = 47 × 8 × (–125) (Commutative property)

= 47 × {8 × (–125)} (Associative property)
= 47 × –1,000 = –47,000

(c) (–17) × 102 = (–17) × (100 + 2)
= (–17) × 100 + (–17) × 2 (Distributive property)
= –1,700 – 34 = –1,734

(d) (–625) × (–47) + (–625) × (–53) = (–625) × {–47 + (–53)}
(Distributive property)
= (–625) × (–100) = 62,500

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