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Properties of Multiplication of Integers - Making Multiplication Easier of Integers

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Making Multiplication Easier:

Consider the following:

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.

Example

Find the following products: (– 18) × (– 10) × 9

(– 18) × (– 10) × 9

= [(–18) × (–10)] × 9

= 180 × 9

= 1620.

Example

Find the following products: (– 20) × (– 2) × (– 5) × 7

(– 20) × (– 2) × (– 5) × 7

= – 20 × (– 2 × – 5) × 7

= [– 20 × 10] × 7

= – 1400.

Example

Find the following products: (– 1) × (– 5) × (– 4) × (– 6)

(–1) × (–5) × (– 4) × (– 6)

= [(– 1) × (– 5)] × [(– 4) × (– 6)]

= 5 × 24

= 120.

Example

Find 16 × 12.

16 × 12

= 16 × (10 + 2)

= 16 × 10 + 16 × 2

= 160 + 32

= 192.

Example

Find (– 23) × 48

(– 23) × 48

= (– 23) × [50 – 2]

= (– 23) × 50 – (– 23) × 2

= (– 1150) – (– 46)

= – 1104

Example

Find (– 35) × (– 98).

(– 35) × (– 98)

= (– 35) × [(– 100) + 2]

= (– 35) × (– 100) + (– 35) × 2

= 3500 + (– 70)

= 3430.

Example

Find 52 × (– 8) + (–52) × 2

52 × (– 8) + (– 52) × 2

= 52 × (– 8) + 52 × (– 2)

= 52 × [(– 8) + (– 2)]

= 52 × [(– 10)]

= – 520.

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Shaalaa.com | Making Multiplication Easier Using Commutative, Associative& Distributive Properties- Part 1

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