**Definition of Multiplicative Property**

- Multiplicative Property of Equality: The two sides of an equation remain equal if they are multiplied by the same number. That is: for any real numbers a, b, and
*c,*if*a*=*b,*then*ac*=*bc*.

- Multiplicative property of Inequality: The two sides of an inequality remain equal if they are multiplied by the same number.

That is, for any real numbers*a, b,*and*c,*if*a > b*then*ac > bc*and if*a <>*then*ac <>*.

- Multiplicative property of Negative One: The product of – 1 and any number results in the opposite of that number.

That is, for any real number a, a × - 1 = - a. - Multiplicative Property of Zero: The product of 0 and any number results in 0.That is, for any real number
*a, a × 0 = 0.*

**Examples of Multiplicative Property**

- Multiplicative Property of Equality:
*x*= 4 ⇒ 3*x*= 12 - Multiplicative Property of Inequality:
*y*< 5="" ⇒="">*y*<> - Multiplicative Property of Negative One: 3 × - 1 = - 3
- Multiplicative Property of Zero: 8 × 0 = 0

**Solved Example on Multiplicative Property**

Which one of these number sentences illustrates multiplicative property of zero?

Choices:

A. 11 × 7 = 7 × 11

B. 18 × 0 = 0

C. 57 + 41.9 = 41.9 + 57

D. 64 + 0 = 64

Correct Answer: B

Solution:

Step 1:The product of zero and any number is zero. [By Zero Property.]

Step 2:So, zero property is related with only multiplication of a number

with 0.

Step 3:The equation 64 + 0 = 64 illustrates the identity property of addition.

Step 4:The equation 11 × 7 = 7 × 11 illustrates the commutative property of multiplication and the equation 57 + 41.9 = 41.9 + 57 illustrates the commutative property of addition.

Step 5:Among the choices, the equation 18 × 0 = 0 only involves multiplication with 0. So, it illustrates zero property.

**Related Terms for Multiplicative Property**

- Multiplicative Property of Equality
- Multiplicative Property of Inequality
- Multiplicative Property of Negative One
- Multiplicative Property of Zero
- Real numbers
- Product
- Opposite