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 <> 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.
Video Examples: Associative property for multiplication
Examples of Multiplicative Property
 Multiplicative Property of Equality: x = 4 ? 3x = 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
Ques: Which one of these number sentences illustrates multiplicative property of zero?
Choices:
A. 11 � 7 = 7 � 11B. 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.
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