Question

Making Multiplication Easier

Consider the following:

(i) We can find (–25) × 37 × 4 as

[(–25) × 37] × 4 = (– 925)× 4 = –3700

Or, we can do it this way,

(–25) × 37 × 4 = (–25) × 4 × 37 = [(–25) × 4] × 37 = (–100) × 37 = –3700

Which is the easier way?

Obviously the second way is easier because multiplication of (–25) and 4

gives –100 which is easier to multiply with 37. Note that the second way

involves commutativity and associativity of integers.

So, we find that the commutativity, associativity and distributivity of integers

help to make our calculations simpler. Let us further see how calculations can

be made easier using these properties.

(ii) Find 16 × 12

16 × 12 can be written as 16 × (10 + 2).

16 × 12 = 16 × (10 + 2) = 16 × 10 + 16 × 2 = 160 + 32 = 192

(iii) (–23) × 48 = (–23) × [50 – 2] = (–23) × 50 – (–23) × 2 = (–1150) – (– 46)

= –1104

(iv) (–35) × (–98) = (–35) × [(–100) + 2] = (–35) × (–100) + (–35) × 2

= 3500 + (–70) = 3430

(v) 52 × (– 8) + (–52) × 2

(–52) × 2 can also be written as 52 × (–2).

Therefore, 52 × (– 8) + (–52) × 2 = 52 × (– 8) + 52 × (–2)

= 52 × [(– 8) + (–2)] = 52 × [(–10)] = –520

There are so many examples by which use we can solve easily solve the

calculations. By using some property of multiplication

Q.1 Find each of the following products:

(i) (–18) × (–10) × 9 (ii) (–20) × (–2) × (–5) × 7

(iii) (–1) × (–5) × (– 4) × (– 6)

Q.2 In a class test containing 15 questions, 4 marks are given for every correct

answer and (–2) marks are given for every incorrect answer.

(i) Gurpreet attempts all questions but only 9 of her answers are correct.

please solve this question​

Answer 1

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