Operations with Rational Numbers

When simplifying expressions with rational numbers,

you must follow the order of operations whileremembering your rules for

positive and negative numbers!

Order of Operations

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Complete at the same time...whichever comes first...from left to right

(ALL Grouping Symbols)

Let's simplify this step by step...

What should you do first?

5 - (-2) = 5 + 2 = 7

What should you do next?

(-3)(7) = -21

What is your last step?

-7 + (-21) = -28

-7 + (-3)[5 - (-2)]

Let's simplify this step by step...

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What should you do first? What should you do second?

What should you do third? What should you do last?

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We can also use Properties to help us.

Commutative Property of Multiplication or Addition• Two or more numbers can be added or multiplied with out changing the sum or product

Associative Property of Multiplication or Addition• For all real numbers a, b, and c, the product or sum is always the same regardless of their grouping.

Evaluate the expression below: -6 x 2 x (-2) x (-5) x (-3)

Use the Commutative or Associative Properties to solve the expression.

One possibility:

You can also use the Distributive Property tohelp you.

Distributive Property:• For all real number a, b, and c, a(b+ c) = ab + bc and

a(b-c) = ab – ac

Examples:

Another example:

-12÷3(-4)

94 Simplify the expression.

95 [-1 - (-5)] + [7(3 - 8)]

96 40 - (-5)(-9)(2)

97 5.8 - 6.3 + 2.5

-3(-4.7)(5-3.2)

Simplify the expression.98

99

100

[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

101

Complete the first step of simplifying. What is your answer?

Now step by step.

[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

102 Complete the next step of simplifying. What is your answer?

[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

103 Complete the next step of simplifying. What is your answer?

[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

104 Complete the next step of simplifying. What is your answer?

105 Simplify the expression.

106 Simplify the expression.

107

108

(-4.75)(3) - (-8.3)109

Solve this one in your groups.

How about this one?

110

111 [(-3.2)(2) + (-5)(4)][4.5 + (-1.2)]

112

113

114

115