Page 1 of 5
Order of Operations
BEFORE
Now
You evaluated expressions
involving one operation.
You’ll evaluate expressions
So you can find the points scored
involving two or more operations. in a video game, as in Example 5.
WHY?
In the Real World
Word Watch
order of operations, p. 18
Music You buy a used guitar for $50. You then
pay $10 for each of 5 guitar lessons. The total
cost can be found by evaluating the expression
50 10 5. Is the total cost $100 or $300?
So that everyone gets the same result when
evaluating an expression, a set of rules called
the order of operations is always followed.
Order of Operations
1. Evaluate expressions inside grouping symbols.
2. Evaluate powers.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
EXAMPLE
1
Following Order of Operations
To find the guitar costs described above, evaluate 50 10 5 .
50 10 5 50 50
100
First multiply 10 and 5.
Then add 50 and 50.
ANSWER The total cost is $100.
EXAMPLE
2
Evaluating a Variable Expression
Evaluate x 3y 3 when x 25 and y 2.
x 3y 3 25 3(23)
18
Chapter 1
Substitute 25 for x and 2 for y.
25 3(8)
Evaluate the power.
25 24 1
Multiply 8 and 3. Then subtract 24 from 25.
Number Sense, Patterns, and Algebraic Thinking
Page 2 of 5
Your turn now
Evaluate the expression.
2. 20 42 2
1. 5 6 5
3. 10 3 33
4. Evaluate a 4b 2 when a 6 and b 5.
Left-to-Right Rule When an expression has a string of additions and
subtractions or a string of multiplications and divisions, you need to
perform the operations in order from left to right.
EXAMPLE
3
Using the Left-to-Right Rule
a. 12 7 3 6 5 3 6
Subtract 7 from 12.
86
Add 5 and 3.
2
Subtract 6 from 8.
b. 54 9 3 6 3
2
Divide 54 by 9.
Divide 6 by 3.
Grouping Symbols Grouping symbols indicate operations that should be
performed first. The most common grouping symbols are parentheses ( )
and brackets [ ]. A fraction bar is also a grouping symbol.
EXAMPLE
with Solving
Thinking of the letters
PEMDAS might help you
remember the order of
operations:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
4
Using Grouping Symbols
a. 4(8 5) 4(3)
12
13 7
20
b. 2p5
10
2
Multiply 4 and 3.
Add 13 and 7. Multiply 2 and 5.
Divide 20 by 10.
c. (4 1)2 p 3 52 p 3
Your turn now
Subtract inside parentheses.
Add inside parentheses.
25 p 3
Evaluate the power.
75
Multiply 25 and 3.
Evaluate the expression.
5. 18 10 5 1
6. (3 7)(6 3)2
Lesson 1.4
8p3
7. 42
Order of Operations
19
Page 3 of 5
EXAMPLE
5
Using Order of Operations
Video Games The tricks and point values for a
skateboarding video game are shown in the table.
You complete one burntwist, three backflips, and
four 360° flips. How many points did you score?
Trick
Burntwist
Backflip
360 flip
Points
500
400
150
Solution
You need to evaluate the expression 1 p 500 3 p 400 4 p 150.
1 p 500 3 p 400 4 p 150 500 1200 600
Multiply first.
1700 600
Add 500 and 1200.
2300
Add 1700 and 600.
ANSWER You scored 2300 points.
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 705
Getting Ready to Practice
1. Vocabulary State the order of operations.
Evaluate the expression.
2. 6 7 p 4
20 8
3. 4
4. 4 p 3 p 23
5. 10 8 5 2
6. 9(16 7)
7. 45 5 3
12 6
8. 31
9. (1 6)(5 2)2
Algebra Evaluate the expression when x 8 and y 2.
10. 4 x p y
11. (x 12) 5
12. 20 y 4 6
13. x y 2 2
14. Guided Problem Solving Entrance to a museum costs $10 for adults
and $7 for students. How much will it cost for 5 adults and 35 students
to enter the museum?
1 Write an expression for the cost for the adults. Write an expression
for the cost for the students.
2 Now write an expression for the total cost for adults and students.
3 Evaluate your expression using order of operations.
20
Chapter 1
Number Sense, Patterns, and Algebraic Thinking
Page 4 of 5
with
Example
1
2
3
4
5
Homework
Exercises
15–23, 30–32
24–26
15–23, 30–32
15–23, 30–32
28–29
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Practice and Problem Solving
Evaluate the expression.
15. 12 2 p 10
16. 40 12 6
17. 7(14 9)
28
18. 73
15 7
19. 31
20. 16 (32 1)
21. 34 9 3
22. (8 2)2 12 6
23. 35 15 5 10
Algebra Evaluate the expression when x 3, y 6, and z 2.
24. 18 x z
xy
25. x
26. 4z 3 y
27. Critical Thinking Insert grouping symbols into the expression
6 7 p 5 8 to make it equal to 73.
28. Magazine Web Site A magazine Web site has a $5 membership fee
and charges $2 for each month. Write and evaluate an expression to
find the cost to join for one year.
Sports
29. Weightlifting In the clean-and-jerk event in the 2000 Summer
Olympics, Cheryl Haworth lifted a 15 kilogram bar, four plates
that each weighed 25 kilograms, and 2 plates that each weighed
15 kilograms. Write and evaluate an expression to find the total
weight that she lifted.
Match the given expression with an expression that has the same
value.
30. 20 42 8
31. 6(12 9)
A. (18 7) p 2
B. 18 p 2 3
32. 21 6 p 3 19
C. 82 p 3 66
Extended Problem Solving In Exercises 33–35,
use the pricing information for Joe’s Joke Shop.
Joe’s Joke Shop
33. Calculate You want to buy a present for each
■
Weightlifting
In the snatch event in the
2000 Summer Olympics,
17-year-old Cheryl Haworth
lifted 125 kilograms. Given
that 1 kilogram is equal to a
little more than 2 pounds,
about how many pounds did
Haworth lift?
Chattering teeth
Hand buzzer
$3
$4
of 6 friends. If you have only $20, could you
buy 6 chattering teeth or 6 hand buzzers?
34. Make a List Suppose you want to buy at least one of each
item. Make a list of all the possible ways of buying 6 presents.
35. Critical Thinking Write and evaluate an expression to find the
total cost of each combination you listed in Exercise 34. Which
combinations of presents could you buy with $20?
Challenge Evaluate the expression.
36. 165 [(4 7) p 5]
37. [(9 34) 30] p 18 38. 175 [35 (5 2)]
Lesson 1.4
Order of Operations
21
Page 5 of 5
Mixed Review
39. To find the length of a theater production, you can use the expression
p i, where p is the length in minutes of the play and i is the length in
minutes of the intermission. Find the length of a production where the
play is 130 minutes long and the intermission is 15 minutes long.
(Lesson 1.2)
Evaluate the power. (Lesson 1.3)
40. 121
41. 132
42. 54
43. 35
Basic Skills Find the difference.
44.
48
29
45.
126
53
46.
301
164
47.
357
258
Test-Taking Practice
48. Multiple Choice In what order should you perform the operations
INTERNET
to correctly evaluate the expression 27 18 32?
State Test Practice
CLASSZONE.COM
A. Evaluate the power, subtract, and then divide.
B. Subtract, evaluate the power, and then divide.
C. Divide, evaluate the power, and then subtract.
D. Evaluate the power, divide, and then subtract.
49. Short Response Evaluate the expression 20 32 p 2 8. How
could you insert parentheses to make the expression equal to 110?
Number Jumble
Copy the expression below. How could you fill in the boxes
with the numbers 1, 2, 3, and 4 to make the expression
have the greatest possible value? the least possible value?
22
Chapter 1
p
Number Sense, Patterns, and Algebraic Thinking