NCERT Class 7 Mathematics

18 MATHEMATICS

TRY THESE

TRY THESE

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.

(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) = –

4 × 3 – 4 × 8 = 12 – 32 = –

So, 4 × (3 – 8) = 4 × 3 – 4 × 8.

Look at the following:

( –5) × [( – 4) – ( – 6)] = ( –5) × 2 = –

[( –5) × ( – 4)] – [ ( –5) × ( – 6)] = 20 – 30 = –

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.

(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 = –