# The given statement and also name the property of real numbers used.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 2E

(a)

To determine

## To complete: The given statement and also name the property of real numbers used.

Expert Solution

The complete statement is ab=ba and the property used is commutative property of real numbers.

### Explanation of Solution

The given statement is ab=_______; ________ Property.

Calculation:

The commutative property states that when a number a is multiplied by another number b then, the order of numbers does not matter.

That is, ab=ba.

Therefore, the complete statement is ab=ba and the property used is commutative property of real numbers.

(b)

To determine

### To complete: The given statement and name the property of real numbers used.

Expert Solution

The complete statement is a+(b+c)=c+(a+b) and the property used is associative property of real numbers.

### Explanation of Solution

Given:

The given statement is a+(b+c)=_______; ________ Property.

Calculation:

The associative property states that when three different numbers are added then order of numbers does not matter (any two numbers can be added first).

That is, a+(b+c)=c+(a+b).

Therefore, the complete statement is a+(b+c)=c+(a+b) and the property used is associative property of real numbers.

(c)

To determine

### To complete: The statement and name the property of real numbers used.

Expert Solution

The complete statement is a(b+c)=ab+ac and the property used is distributive property of real numbers.

### Explanation of Solution

Given:

The given statement is a(b+c)=______; _________ Property.

Calculation:

The distributive property states that a real number a multiplied by a sum of two numbers (b+c) has the same result when the number a is multiplied by each of the terms and then added.

a(b+c)=ab+ac(b+c)a=ab+ac

Therefore, the complete statement is a(b+c)=ab+ac and the property used is distributive property of real numbers.

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