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.


Video Examples: Associative property for multiplication


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

Ques: 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.
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