MULTIPLICATIVE PROPERTY

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=""><>

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.

Quick Summary

Multiplying both sides of an equation by the same number maintains equality.
Multiplying both sides of an inequality by the same positive number maintains the inequality. Multiplying by a negative number reverses the inequality.
Multiplying any number by -1 results in its opposite.
Multiplying any number by 0 results in 0.

\[ a \times 0 = 0 \]

🍎 Teacher Insights

Use concrete examples and visual aids to illustrate the multiplicative property, especially when dealing with inequalities and negative numbers. Emphasize the importance of applying the operation to *both* sides of the equation or inequality.

🎓 Prerequisites

Basic multiplication
Understanding of equality and inequality
Knowledge of real numbers

Check Your Knowledge

Q1: Which equation illustrates the multiplicative property of zero?

A. 5 + 0 = 5 B. 7 × 1 = 7 C. 9 × 0 = 0 D. 3 + 2 = 2 + 3

Q2: If x = 6, what is the value of 2x according to the multiplicative property of equality?

A. 3 B. 4 C. 8 D. 12

Frequently Asked Questions

Q: What is the difference between the multiplicative property of equality and the additive property of equality?
A: The multiplicative property of equality states that if you multiply both sides of an equation by the same number, the equation remains true. The additive property states that if you add the same number to both sides of an equation, the equation remains true.

Q: Why does multiplying by a negative number reverse the inequality sign?
A: Multiplying by a negative number effectively flips the number line. For example, 2 > 1, but -2 < -1. The order is reversed.