Page 16 - pdf N.C.E.R.T INTEGERS CH 1

16 MATHEMATICS

What are your observations? The above examples suggest multiplication is
commutative for integers. Write five more such examples and verify.
In general, for any two integers a and b,

a × b = b × a

1.5.3 Multiplication by Zero

We know that any whole number when multiplied by zero gives zero. Observe the following
products of negative integers and zero. These are obtained from the patterns done earlier.
(–3) × 0 = 0
0 × (– 4) = 0
– 5 × 0 = _____

0 × (– 6) = _____
This shows that the product of a negative integer and zero is zero.
In general, for any integer a,
a × 0 = 0 × a = 0

1.5.4 Multiplicative Identity

We know that 1 is the multiplicative identity for whole numbers.
Check that 1 is the multiplicative identity for integers as well. Observe the following
products of integers with 1.
(–3) × 1 = –3 1 × 5 = 5
(– 4) × 1 = _____ 1 × 8 = _____

1 × (–5) = _____ 3 × 1 = _____
1 × (– 6) = _____ 7 × 1 = _____
This shows that 1 is the multiplicative identity for integers also.
In general, for any integer a we have,
a × 1 = 1 × a = a

What happens when we multiply any integer with –1? Complete the following:
(–3) × (–1) = 3
3 × (–1) = –3
0 is the additive identity whereas 1 is the
(– 6) × (–1) = _____ multiplicative identity for integers. We get

(–1) × 13 = _____ additive inverse of an integer a when we multiply
(–1) × (–25) = _____ (–1) to a, i.e. a × (–1) = (–1) × a = – a
18 × (–1) = _____
What do you observe?
Can we say –1 is a multiplicative identity of integers? No.