Page 30 - Maths Class 06

Study the following carefully:
8 ÷ 4 = 2
0 ÷ 4 = 0
8
8 ÷ 3 =
3
8
We see that 8 ÷ 3, i e. . is not a whole number.
3
Hence, the closure property does not hold good for the division of whole numbers.
For example, 6 ÷ 3 = 2 (A whole number)

4 ÷ 2 = 2 (A whole number)
2
2 ÷ 9 = (Not a whole number)
9

Prop erty 2.
Commutative Property : The quotient of a whole number and another non-zero whole number changes if
the dividend and the divisor interchange their places.
For example, (i) 16 ÷ 2 = 8 (A whole number) (ii) 2 ÷ 1 = 2 (A whole number)
2 1
2 ÷ 16 = (Not a whole number) 1 ÷ 2 = (Not a whole number)
16 2
Thus, 16 ÷ 2 ¹ 2 ÷ 16. Thus, 2 ÷ 1 ¹ 1 ÷ 2.
Hence, the division in whole numbers in not commutative.

Prop erty 3.
Property of One : If ‘a’ is a whole number, then a ÷ 1 = a.

For example, (a) 6 ÷ 1=6 (A whole number)
(b) 2 ÷ 1 = 2 (A whole number)
(c) 1 ÷ 1 = 1 (A whole number)

Prop erty 4.

If ‘a’ is a non-zero whole number, then a ÷ a = 1.
For example,
(a) 3 ÷ 3 = 1 (b) 2 ÷ 2 = 1 (c) 4 ÷ 4 = 1

Prop erty 5.

If zero is divided by any whole number except zero, the quotient is zero.
For example,
(a) 0 ÷ 2 = 0 (b) 0 ÷ 4 = 0 (c) 0 ÷ 8 = 0

Prop erty 6.

If three whole numbers are taken in a particular order and the quotient of the first and the second is
divided by the third, then the result is not the same if the first is divided by the quotient of the second and
the third.

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