Order of Operations

Also known to as PEMDAS

EXAMPLE 1 Following Order of Operations

Music

You buy a used guitar for $50. You then pay $10 for each of five guitar lessons. The total cost can be found by evaluating the expression

50 + 10 x 5. Is the total cost $100 or $300?

= 50 + 50

EXAMPLE 1

To find the guitar costs described, evaluate 50 + 10 5.

50 + 10 5 First multiply 10 and 5.

= 100 Then add 50 and 50.

ANSWER The total cost is $100.

Following Order of Operations

EXAMPLE 2 Evaluating a Variable Expression

Substitute 25 for x and 2 for y.

Evaluate the power.

Multiply 8 and 3.

= 1 Subtract 24 from 25.

x 3y3 – = 25 3(23 ) –

= 25 3(8) –

= 25 24 –

Evaluate x 3y3 when x = 25 and y = 2.–

GUIDED PRACTICE for Examples 1 and 2

Evaluate the expression.

1.

5 + 6 x 5

35ANSWER

2.

20 42 2–

12ANSWER

3.

10 • 3 + 33

57ANSWER

GUIDED PRACTICE

4.

Evaluate a + 4b2 when a = 6 and b = 5.

106ANSWER

for Examples 1 and 2

EXAMPLE 3 Using the Left-to-Right Rule

5 + 3 - 6 a. 12 7 + 3 - 6 = – Subtract 7 from 12.

= 8 6 – Add 5 and 3.

= 2 Subtract 6 from 8.

6 ) • 3 = Divide 54 by 9.

6 • 3 = 18 Multiply 6 and 3.

54 9 (3+ b.

EXAMPLE 4 Using Grouping Symbols

Subtract inside parentheses. = 4(3)

= 12 Multiply 4 and 3.

=2010

Evaluate expressions grouped by fraction bar.

= 2 Divide 20 by 10.

Add inside parentheses.

Evaluate the power.

= 75 Multiply 25 and 3.

= 52 • 3

= 25 • 3

b.

13 + 72 5

a.

4(8 5) –

c.

(4 + 1)2•3

GUIDED PRACTICE for Examples 3 and 4

Evaluate the expression.

5.

18 10 + 5 - 1–

12ANSWER

6.

(3 7) (6 - 3)2+

90ANSWER

7.

8 3

4 + 2

4ANSWER

GUIDED PRACTICE

Evaluate the expression.

8.

25 6 14 3– +–

8ANSWER

9.

16 2 11

88ANSWER

10.

16(9 + 1) - 30

130ANSWER

for Examples 3 and 4

EXAMPLE 5 Standardized Test Practice

EXAMPLE 5

SOLUTION

= 500 + 1200 + 600 Multiply first.

= 1700 + 600 Add 500 and 1200.

= 2300 Add 1700 and 600.

ANSWER You score 2300 points. The correct answer is D.

You need to evaluate the expression 1 • 500 + 3 • 400 + 4 • 150.

1 500 + 3 400 + 4 150

Standardized Test Practice

GUIDED PRACTICE for Example 5

11.

What If? In Example 5, suppose you complete two burntwists, two backflips, and one 360° flip. How many points do you score?

1950 points.ANSWER