Properties of Division

Properties of Division

Can you find the value when (–5) is divided by 3? The value is not an integer. Clearly, the collection of integers is not ‘closed’ under division. Test it by taking 5 more examples

To test the commutative property of division on integers, let us take –5 and 3.

(–5) ÷ 3 ≠ 3 ÷ (–5). Also 5 ÷ (–3) ≠ (–3) ÷ 5 and (–5) ÷ (–3) ≠ (–3) ÷ (–5)

Therefore, division of integers are not commutative. Verify this with 5 more examples. Since the commutative property is not true, associative property does not hold.

Let us take integers, –7 and 1.

(–7) ÷ 1 = – 7 but 1 ÷ (–7) ≠ – 7.

Let us take (–6) ÷ (–1) and 6 ÷ (–1).

(–6) ÷ (–1) = 6 and 6 ÷ (–1) = – 6.

Therefore, when we divide an integer by –1, we will not get the same integer.

Hence, there does not exist an identity for division of integers.

Take any five integers and verify the above.

Note

An integer divided by zero is meaningless. But zero divided by a non-zero integer is zero.