Chapter 8.7, Problem 60STP

To determine

To choose: The correct equation that illustrates the Commutative property.

Answer to Problem 60STP

The correct option is (A)

Explanation of Solution

Given Information: The given equations are $ab=ba$ , $a\left(bc\right)=\left(ab\right)c$ , $ab=ab$ , $a\left(b+c\right)=ab+ac$

Concept used:

Use the definition of commutative property of multiplication. The commutative property states that $a\times b=b\times a$

Consider the first equation $ab=ba$

In the given equation the same variables are multiplied with their order changed $ab=ba$ .

Therefore, the equation illustrates the commutative property.

Consider the second equation $a\left(bc\right)=\left(ab\right)c$

In the given equation grouping of the variables is changed. This property is called associative property. Therefore, this equation does not illustrate the commutative property.

Consider the third equation $ab=ab$ .In the given equation both the sides are same. Also, the order of the variables is same. Therefore, the equation does not illustrate the commutative property.

Consider the equation $a\left(b+c\right)=ab+ac$ In the given equation $a$ distributes over $b$ and $c$ .

The product distributes over the addition.

Therefore, the equation does not illustrate the commutative property.