Question

write the properties of divison of integers
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Answer 1

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The following properties of division of integers are:

(i) If x and y are integers, then x ÷ y is not necessarily an integer.

For example; 16 ÷ 3, -17 ÷ 5 are not integers.

(ii) If x is an integer different from 0, then x ÷ x = 1.

(iii) For every integer x, we have x ÷ 1= x.

(iv) If x is a non-zero integer, then 0 ÷ x = 0.

(v) If x is an integer, then x ÷ 0 is not meaningful.

(vi) If x, y, z are non-zero integers, then (x ÷ y) ÷ z ≠ x ÷ (y ÷ z), unless z = 1.

(vii) If x, y, z are integers, then

• (a) x > y ⇒ x ÷ z > y ÷ z, if z is positive.

• (a) x > y ⇒ x ÷ z < y ÷ z, if z is negative.

Answer 2

Answer:

+ ÷ + = +

- ÷ - = +

+ ÷ - = -

- ÷ + = -

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