Problem 73 - Introductory and Intermediate Algebra for College Students 4th

Question

State the multiplication property of equality and give an example.

Step-by-Step Solution

Answer

The multiplication property of equality states that if you multiply both sides of an equation by the same number, the equation remains balanced. An example of this is when we start with the equation '5 = 5', and multiply both sides by the number 2, resulting in '10 = 10'.

Step 1: State the Multiplication Property of Equality

The multiplication property of equality states that if you multiply both sides of an equation by the same number, the sides remain equal. In other words, if \( a = b \), then \( a \cdot c = b \cdot c \), where c is a constant.

Step 2: Provide an Example

If we have an equation like \( 5 = 5 \), we can multiply both sides by 2, thus standing true to the multiplication property of equality: \( 5 \cdot 2 = 5 \cdot 2 \), which simplifies to \( 10 = 10 \). Here, the constant c is 2.