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- Pre-Algebra Chapter 5.1 (A) Properties of Real Numbers

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Describe the Cummutative Property of Addition

When you add two numbers, the numbers can be added in any order and the sum will be the same.

Give an example of the Communitive Property of Addition

a+b=b+c

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Define the Commutative Property of Multiplication

When we multiply two numbers, the numbers can be multiplied in any order and the product will be the same.

Give an example of the Communitive Property of Multiplication

a.b=b.a

Define the Associative Property of Addition

When we add three or more numbers, the numbers can be grouped in any order; the sum is the same.

Give an example of the Associative Property of Addition

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

Define the Associative Property of Multiplication

When we multiply three or more numbers, the numbers can be grouped in any order; the product is the same.

Give an example of the Associative Property of Multiplication

(a.b).c = a.(b.c)

Define the Addition Property of Zero

The sum of a number and zero is the number.

Give an example of the Addition Property of Zero

a+o=o+a=a

Define the Multiplication Property of Zero

The product of a number and zero is the number.

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Give an example of the Multiplication Property of Zero

a.o=o.a=a

Define The Multiplication Property of One

The product of a number and 1 is the number

Give an Example of The Multiplication Property of One

a.1=1.a=a

Define The Inverse Property of Addition

The sum of a number and its inverse is 0

Give and Example of The Inverse Property of Addition

a+(-a) = (-a) + a = 0

Define The Inverse Property of Multiplication

The product of a non zero number and its inverse is 1

give and example of The Inverse Property of Multiplication

a . 1/a = 1/a . a = 1

The properties of real numbers can be used to rewrite a variable expression in a simpler form. This process is called:

simplifying the variable expression

Simplify 5.(4x) using the associative property of multiplication

5*(4x) = (5*4)x

= 20x

Simplify (6x) . 2 using the communitive property of Multiplication

(6x) . 2 = 2* (6x)

= (2*6)x

= 12x

Simplify: (5y)(3y) using the communitive and associateive properties of addition

(5y)(3y) = 5*y*3*y

= 5*3*y*y

= (5*3)(y*y)

15y(second power)

Simplify -5(7b)

-5(7b) = (-5*7)b

=-35b

Simplify (-4r)(-9t)

(-4r)(-9t) = [(-4)(-9)](r*t)

= 36rt

Simplify (-8)(-z)

(-8)(-z) =(-8)(-1z)

=[(-8)(-1)]z

=8z

Simplify -5y +5y + 7

-5y + 5y + 7= 0+7

=7

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