# To state: The properties of the commutative property of a real numbers

### 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, Problem 2RCC

(A)

To determine

## To state: The properties of the commutative property of a real numbers

Expert Solution

### Explanation of Solution

Given:

The commutative property

a+b=b+a

Concept used:

Commutative property of addition and multiplication

a+b=b+aab=ba

Calculation:

Commutative property:-The commutative property of addition

That is two numbers are being added, their order can be changed without affecting the sum

Counter example :-

a+b=b+a7+3=3+7

The commutative property of multiplication

That is two numbers are being multiplied, their order can be changed without affecting the product

Counter example :-

ab=ba35=53

(B)

To determine

Expert Solution

### Explanation of Solution

Given:

The associative property

(a+b)+c=a+(b+c)

Concept used:

Associative property of addition and multiplication

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

Calculation:

Associative property:-The associative property of addition

That is three numbers are being added, their order can be changed without affecting the sum

Counter example :-

(a+b)+c=a+(b+c)(2+4)+7=2+(4+7)

The associative property of multiplication

That is three numbers are being multiplied, their order can be changed without affecting the product

Counter example :-

(ab)c=a(bc)(37)5=3(75)

(C)

To determine

Expert Solution

### Explanation of Solution

Given:

The distributive property

a(b+c)=ab+ac

Concept used:

Distributive property

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

Calculation:

Distributive property:-the multiply a number by a sum of two numbers

If multiply the number by each of the term and add the results

Counter example :-

a(b+c)=ab+ac2(3+5)=23+25(b+c)a=ab+ac(3+5)2=23+25

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