Question

(-3)×(-5)=(-5)×(-3)=15 which property of whole numbers is used ​

Answer 1

commutative property is used

Answer 2

Properties of Multiplication

Closure Property

Multiplication of two whole numbers will result in a whole number. Suppose, a and b are the two whole numbers and a × b = c, then c is also a whole number. Let a = 10, b = 5, 10 × 5 = 50 (whole number). The whole number is closed under multiplication.

Commutative Property

The value of the product does not change when the order of multiplication gets changed. This is the commutative property of multiplication. Let the two whole numbers be a and b, then a × b = b × a ⇒ 4 × 9 = 36 = 9 × 4.

Associative Property

When we multiply three or more whole numbers, the value of the product remains the same when they are grouped in any manner. The associative property of multiplication holds for whole numbers. Thus, if ‘a’, ‘b’, and ‘c’ are three whole numbers, then a × (b × c) = (a × b) × c = (a × c) × b. For example, 6 × (7 × 2) = (6 × 7) × 2 = (6 × 2) × 7 = 84.

Multiplicative Identity

When we multiply 1 with any whole number, the product is the number itself. 1 is the multiplicative identity of the whole numbers. If w is a whole number, then w × 1 = 1 × w.

Multiplicative Property of Zero

The product of a whole number and 0 is always 0 i.e., w × 0 = 0 = 0 × w. For example, 813 × 0 = 0 = 0 × 813.

Distributive Property of Multiplication over Addition

This property shows that multiplication of a whole number is distributed over the sum of the whole numbers. If a, b, and c are the three whole numbers. We have, a × (b + c) = (a × b) + (a × c). Let a = 10, b = 20 and c = 5 ⇒ 10 × (20 + 5) = 250 and (10 × 20) + (10 × 5) = 200 + 50 = 250.

Distributive Property of Multiplication over Subtraction

This property tells that multiplication of a whole number is distributed over the difference of the whole numbers. Suppose ‘a’, ‘b’, and ‘c’ are three whole numbers. From this property we have,a × (b − c) = (a × b) − (a × c). Let a = 10, b = 20 and c = 5 ⇒ 10 × (20 − 5) = 150 and (10 × 20) − (10 × 5) = 200 − 50 =