Page 1 of 4
Variables and Expressions
BEFORE
Now
WHY?
You simplified numerical
expressions.
You’ll evaluate variable
expressions.
So you can estimate bamboo
growth, as in Ex. 35.
You can evaluate an expression by using a number strip.
Word Watch
variable, p. 9
variable expression, p. 9
evaluate, p. 9
1 Cut a long strip of paper. Write the numbers
1 through 9 on the strip.
2 Write “n 6” on the remaining part of
the paper. Cut two vertical slits (big enough
for the number strip to fit through) on each
side of the n.
3 Slide the strip through the slits so that one
number at a time shows. Write the resulting
expression for each number. Then simplify.
Repeat the activity for the given expression.
1. n 1
2. n 2
In the activity, you substituted numbers for the variable n.
A variable is a letter that is used to represent one or more numbers.
A variable expression , like n 6, consists of numbers, variables, and
operations. To evaluate a variable expression, you substitute values
for the variables and then simplify the resulting numerical expression.
EXAMPLE
1
Evaluating Variable Expressions
a. Evaluate x 4 when x 9.
b. Evaluate y 3 when y 7.
Solution
a. x 4 9 4
13
Add.
b. y 3 7 3
4
Your turn now
1. 7 m
Substitute 9 for x.
Substitute 7 for y.
Subtract.
Evaluate the expression when a 3 and m 9.
2. a 28
3. 10 a
Lesson 1.2
4. m 5
Variables and Expressions
9
Page 2 of 4
Multiplication and Division Expressions
The expression 2 5 can also be written as 2 p 5. There are
several different ways you can write multiplication and division
expressions.
Multiplication:
x
is another way of writing x 4.
4
Division:
tch Out!
Wa
EXAMPLE
2
5n is another way of writing 5 p n.
ab is another way of writing a p b.
3(7) is another way of writing 3 p 7.
Evaluating Variable Expressions
a. Evaluate 4n when n 6.
Avoid using the
multiplication symbol in a variable expression.
It could be confused with
the variable x.
z
b. Evaluate 2 when z 8.
Solution
a. 4n 4(6)
24
Your turn now
Substitute 6 for n.
Multiply.
6. 18t
3
8
4
Substitute 8 for z.
Divide.
Evaluate the expression when s 5 and t 10.
5. 9s
EXAMPLE
z
b. 2 2
100
7. t
Evaluating Expressions with Two Variables
Ice Hockey To find the number of points earned
by a hockey player, you can evaluate the expression
g a, where g is the number of goals scored and a
is the number of assists. Find the number of points
earned by a hockey player with 12 goals and
29 assists.
Solution
g a 12 29
41
Substitute 12 for g and 29 for a.
Add.
ANSWER The hockey player earned 41 points.
10
Chapter 1
45
8. s
Number Sense, Patterns, and Algebraic Thinking
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 705
Getting Ready to Practice
1. Vocabulary Give two examples of a variable expression.
Evaluate the expression when x 7 and y 15.
2. y 9
3. x 6
4. 4y
5. 8 x
y
6. 5
7. 3x
8. 20 y
14
9. x
10. Find the Error Describe and
correct the error in evaluating
2a when a 3.
2a 23
11. Dance You pay $8 to see a modern dance show. The expression s 8,
where s is the cost of snacks you buy at intermission, can be used to
find the total cost of going to the show. Find the total cost if you buy
snacks that cost $3.
Practice and Problem Solving
12. Writing Describe how to evaluate a variable expression.
13. Write the expression 4 8 in two other ways.
Evaluate the expression for the given value of the variable.
with
Example
1
2
3
Homework
Exercises
14–23
14–22, 24, 34
26–33, 35
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
14. x 14 when x 8
15. y 5 when y 13
16. 7r when r 4
6
17. when s 3
s
t
18. when t 18
3
19. 18 a when a 17
20. y 11 when y 7
21. 8b when b 9
22. 24 x when x 15
23. Television A TV show is an hour long with commercials. To find how
many minutes long the show is without commercials, you can evaluate
the expression 60 c, where c is the number of minutes of
commercials. If there are 12 minutes of commercials, how many
minutes long is the show without commercials?
24. Footbag To play footbag, you kick a small bean bag to keep it in the
air. The expression 3m, where m is the number of minutes played, can
be used to find the calories burned by a 100 pound person playing
footbag. Find the calories burned by a 100 pound person playing
footbag for 45 minutes.
Lesson 1.2
Variables and Expressions
11
Page 4 of 4
25. Critical Thinking Find the value of c that makes the expression
c 12 equal to 20.
Science
Evaluate the expression when x 3, y 9, m 13, and p 25.
26. p m
27. y p
28. m p
29. m y
30. xy
31. mx
y
32. x
33. m y
w
34. Pluto The expression , where w is weight in pounds on Earth, can
17
be used to approximate weight in pounds on Pluto. If Tom weighs
153 pounds on Earth, find his approximate weight on Pluto.
35. Bamboo You can predict the growth for a stem of bamboo by
evaluating the expression gn, where g is the average number of inches
grown each day and n is the number of days. Predict the amount of
growth in one week for bamboo that grows an average of 12 inches
each day.
36. Compare Explain the difference between a number and a variable.
■
Bamboo
It’s a good thing that bamboo
grows so fast because
pandas eat up to 83 pounds
of bamboo a day! How
many pounds of food do
you estimate you eat in
one day?
Challenge Evaluate the expression when x 20, y 12, and
z 15.
37. 9 z x
38. 7yz
39. xyz
40. x y z
43. 45 17
44. 330 42
Mixed Review
Find the product. (p. 689)
41. 233 7
42. 546 8
Describe the pattern. Then write the next three numbers. (Lesson 1.1)
45. 1, 8, 15, 22, . . .
46. 7, 14, 28, 56, . . .
47. 99, 88, 77, 66, . . .
Basic Skills Find a low and high estimate for the quotient.
48. 28 9
49. 230 6
50. 5000 22
51. 7632 5
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
52. Multiple Choice Which of the following is not a variable expression?
A. 4n
B. n m
C. n 4
D. 4 3
53. Multiple Choice What is the value of the expression x y when x 15
and y 21?
F. 6
12
Chapter 1
G. 30
Number Sense, Patterns, and Algebraic Thinking
H. 36
I. 42