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Multiplicative Property

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 < b then ac < bc.

• 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:
• Multiplicative Property of Inequality:
• 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

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