Integers

Properties of Division of Integers

1. The integers are not closed under division. Look at the following table.

ExpressionValueInference
(– 8) ÷ (– 4) = 2An integer
(– 4) ÷ (– 8)= 1/2 Not an integer
(–250) ÷ 750 = – 1/3 Not an integer
100 ÷ (– 1000) = –1/10  Not an integer

2. The division is not commutative for integers. Look at the following table.

Expression 1Expression 2Inference
(– 8) ÷ (– 4) = 2(– 4) ÷ (– 8) = 1/2(– 8) ÷ (– 4) (– 4) ÷ (– 8)
(– 9) ÷ 33 ÷ (– 9)(– 9) ÷ 3 3 ÷ (– 9)
30 ÷ (– 6)(– 6) ÷ 30 = 30 ÷ (– 6) (– 6) ÷ 30

3. Like whole numbers, any integer divided by zero is meaningless. In other words, for any integer a, a ÷ 0 is not defined.

ExpressionInference
8 ÷ 0 Not defined
(– 9) ÷ 0Not defined
(– 1632) ÷ 0Not defined

4. Zero divided by an integer other than zero is equal to zero. In other words, for any integer a, 0 ÷ a = 0 for a 0.

ExpressionValue
0 ÷ 3 0
0 ÷ (– 9)0
0 ÷ (– 1632) 0

5. When we divide a whole number by 1 it gives the same whole number. Similarly, any integer divided by 1 gives the same integer. In general, for any integer a, we have a ÷ 1 = a.

ExpressionValue
(– 8) ÷ 1  = (– 8)
(–11) ÷ 1 = –11
(–13) ÷ 1  = –13

6. When we divide an integer by (–1) it gives the same integer with changed sign. In general, for any integer a, we have a ÷ (–1) = –a.

ExpressionValue
8 ÷ (–1) = – 8
(–25) ÷ (–1) = 25
– 48 ÷ (–1)= 48

6 comments

  1. Sir , I am from class 8
    Maths was really easy
    I solved all in first attempt
    Plz upload more interesting maths for us , as I have shared the post with my friends

    Liked by 1 person

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