Page 110 - Basic College Mathematics with Early Integers

SE CT I O N 1. 9 I EXPONENTS, SQUARE ROOTS, AND ORDER OF OPERATIONS 87

Objective Using the Order of Operations

Suppose that you are in charge of taking inventory at a local cell phone store. An
employee has given you the number of a certain cell phone in stock as the expression
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6 + 2 30
To calculate the value of this expression, do you add first or multiply first? If you
add first, the answer is 240. If you multiply first, the answer is 66.

Mathematical symbols wouldn’t be very useful if two values were possible for
one expression. Thus, mathematicians have agreed that, given a choice, we multiply
first.
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6 + 2 30 = 6 + 60 Multiply.
= 66 Add.
This agreement is one of several order of operations agreements.

Order of Operations

1. Perform all operations within parentheses ( ), brackets [ ], or other grouping
symbols such as fraction bars or square roots, starting with the innermost set.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right.
4. Add or subtract in order from left to right.

Below we practice using order of operations to simplify expressions.

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Example 12 Simplify: 2 4 - 3 , 3 PRACTICE 12
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Simplify: 9 3 - 8 , 4
Solution: There are no parentheses and no exponents, so we start by
multiplying and dividing, from left to right.
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2 4 - 3 , 3 = 8 - 3 , 3 Multiply.
= 8 - 1 Divide.
= 7 Subtract.

Work Practice 12

Answer
12. 25