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Example 5: Find the product of the following using suitable property.
(a) (–13) × 196

(b) (–14) × (–15) × (–16) Quick Check
(c) (–7) × [(–8) + 9] × (–5) Discuss with your teacher how to
(d) (–13) × (–102) + (–13) × (–8) find the multiplicative inverse of the
following without actually solving.
Solution: (a) (–13) × 196 = (–13) × (200 – 4)
(–7) × (–25) + (–7) × 35
= (–13) × 200 – (–13) × 4
[Using Distributive property of integers over subtraction]

= –2600 – (–52)
= –2600 + 52
= – 2548
(b) (–14) × (–15) × (–16) = [(–14) × (–15)] × (–16)

[Using Associative property of multiplication]
= 210 × (–16)
= – 3360

(c) (–7) × [(–8) + 9] × (–5) = (–7) × 1 × (–5)
= [(–7) × 1] × (–5)
[Using Associative property of multiplication]
= (–7) × (–5) = 35
(d) (–13) × (–102) + (–13) × (–8)

= (–13) × [(– 102) + (–8)]
[Using Distributive property of integers over addition]

= (–13) × (– 110)
= 1430

Quick Check
Write the name of the property used for the following statements.
(a) (–2) × [(–4) – (–5)] = (–2) × (–4) – (–2) × (–5) ..................
(b) {(–3) × (–7)} × (–2) = (–3) × {(–7) × (–2)} ..................
(c) 0 × (–7) = 0 ..................
(d) (–15) × 1 = –15 ..................

Example 6: A tanker contains 964 litres of oil. Due to leakage in the tanker, the
quantity of oil decreases at the rate of 3 litres per hour. How much oil will be left
in the tanker after 12 hours?
Solution: Total quantity of oil in the tanker = 964 litres.

Since, due to leakage in the tanker, the quantity of oil decreases at the rate of 3 litres per hour.
Therefore, the quantity of oil leaked from the tanker in 12 hours due to leakage = (3 × 12) litres
= 36 litres
Thus, the quantity of oil left in the tanker after 12 hours = (964 – 36) litres = 928 litres

Mathematics-7 16