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: x = 4 ⇒ 3x = 12
• Multiplicative Property of Inequality: y < 5 ⇒ 2y < 10
• 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

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