Page 18 - N.C.E.R.T PDF INTEGERS cl 7

18 MATHEMATICS

Can we say that the distributivity of multiplication over addition is true for integers
also? Yes.
In general, for any integers a, b and c,
a × (b + c) = a × b + a × c

Take atleast five different values for each of a, b and c and verify the above Distributive
property.

TRY THESE

(i) Is 10 × [(6 + (–2)] = 10 × 6 + 10 × (–2)?

(ii) Is (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)?

Now consider the following:
Can we say 4 × (3 – 8) = 4 × 3 – 4 × 8?
Let us check:
4 × (3 – 8) = 4 × (–5) = –20
4 × 3 – 4 × 8 = 12 – 32 = –20
So, 4 × (3 – 8) = 4 × 3 – 4 × 8.
Look at the following:

( –5) × [( – 4) – ( – 6)] = ( –5) × 2 = –10
[( –5) × ( – 4)] – [ ( –5) × ( – 6)] = 20 – 30 = –10
So, ( –5) × [( – 4) – ( – 6)] = [( –5) × ( – 4)] – [ ( –5) × ( – 6)]
Check this for ( –9) × [ 10 – ( –3)] and [( –9) × 10 ] – [ ( –9) × ( –3)]
You will find that these are also equal.
In general, for any three integers a, b and c,

a × (b – c) = a × b – a × c

Take atleast five different values for each of a, b and c and verify this property.

TRY THESE

(i) Is 10 × (6 – (–2)] = 10 × 6 – 10 × (–2)?
(ii) Is (–15) × [(–7) – (–1)] = (–15) × (–7) – (–15) × (–1)?

1.5.7 Making Multiplication Easier

Consider the following:
(i) We can find (–25) × 37 × 4 as
[(–25) × 37] × 4 = (– 925)× 4 = –3700