Question

Explain properties of multiplication and division of integers with one example

Answer 1

Answer:

Commutative property of multiplication: Changing the order of factors does not change the product. For example, 4 × 3 = 3 × 4 4 \times 3 = 3 \times 4 4×3=3×44, times, 3, equals, 3, times, 4. Associative property of multiplication: Changing the grouping of factors does not change the product

Step-by-step explanation:

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Answer 2

$\huge\bold{Properties\:of\:multiplication}$

Commutative property of multiplication: Changing the order of factors does not change the product. For example, 4 × 3= 3 × 4

Associative property of multiplication: Changing the grouping of factors does not change the product. For example, (2 × 3) × 4= 2 ×(3 × 4)

Identity property of multiplication: The product of 111 and any number is that number. For example, 7 × 1= 7

$\huge\bold{Properties\:of\:division}$

(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.