Beginning Algebra, 11th Edition

If addition is to be performed first, the parentheses should group

equals or 21.

Other grouping symbols are brackets braces and fraction bars. (For

example, in the expression is “grouped” in the numerator.)

To work problems with more than one operation, we use the following order of

operations.This order is used by most calculators and computers.

8 - 32 , 8 - 2

34 , 56 ,

15 + 22 # 3 7 #3,

5 + 2.

16 CHAPTER 1 The Real Number System

Order of Operations

If grouping symbols are present,simplify within them, innermost first (and

above and below fraction bars separately), in the following order.

Step 1 Apply all exponents.

Step 2 Do any multiplicationsor divisionsin the order in which they occur,

working from left to right.

Step 3 Do any additionsor subtractionsin the order in which they occur,

working from left to right.

If no grouping symbols are present,start with Step 1.

NOTE In expressions such as or multiplication is understood.

Using the Rules for Order of Operations

Find the value of each expression.

(a)

Multiply.

= 34 Add.

= 4 + 30

4 + 5 # 6

EXAMPLE 2

3172 1 - 521 - 42 ,

Be careful!

Multiply first.

(b)

Work inside parentheses.

Multiply.

(c)

Multiply, working from left to right.

= 58 Add.

= 48 + 10

6 # 8 + 5 # 2

= 153

= 91172

916 + 112

(d)

Work inside parentheses.

Multiply.

= 43 Add.

= 22 + 21

= 21112 + 7 # 3

215 + 62 + 7 # 3

(e)

Apply the exponent.

Multiply.

Subtract.

= 6 Add.

= 1 + 5

= 9 - 8 + 5

= 9 - 2 # 2 # 2 + 5

9 - 23 + 5

23 = 2 # 2 #2,not 2#3.

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