1-1 Variables and Expressions
Holt Algebra 1

1-1 Variables and Expressions
A variable is a letter used to represent a value that can change.
2 x

9
A constant is a value that does not change.
2 x

9
A numerical expression contains only constants and operations.
An algebraic expression may contain variables, constants, and operations.
2 x

9
Holt Algebra 1

1-1 Variables and Expressions
You will need to translate between algebraic expressions and words to be successful in math.
+


Holt Algebra 1

1-1 Variables and Expressions
Writing Math
These expressions all mean “2 times y”:
2y 2(y)
2•y (2)(y)
(2)y
Holt Algebra 1

1-1 Variables and Expressions
Check It Out!
Example 1
Give two ways to write each algebra expression in words.
1b. 1a.
4 - n
4 decreased by n
n less than 4 the quotient of t and 5
t divided by 5
1c. 9 + q the sum of 9 and q
q added to 9
1d. 3(h) the product of 3 and h
3 times h
Holt Algebra 1

1-1 Variables and Expressions
Example 2A: Translating from Words to Algebra
John types 62 words per minute. Write an expression for the number of words he types in
m minutes.
62 m
Holt Algebra 1

1-1 Variables and Expressions
Example 2B: Translating from Words to Algebra
Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age y

4
Holt Algebra 1

1-1 Variables and Expressions
Example 2C: Translating from Words to Algebra
Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars.
Solving a literal equation—Write c in terms of d.
5 c
 d
5 5
Holt Algebra 1 c
 d
5

1-1 Variables and Expressions
Check It Out!
Example 2a
Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours.
65 t
Holt Algebra 1

1-1 Variables and Expressions
To evaluate an expression is to find its value.
Substitute numbers for the variables and simplify.
Holt Algebra 1

1-1 Variables and Expressions
Example 3: Evaluating Algebraic Expression
Evaluate each expression for a = 4, b =7, and
c = 2.
A. b – c
7 5
B. ac
4
 
8
Holt Algebra 1

1-1 Variables and Expressions
Example 4a: Recycling Application
Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag.
Write an expression for the number of bottles needed to make s sleeping bags.
85 s
Holt Algebra 1

1-1 Variables and Expressions
85 s
Find the number of bottles needed to make
20, 50, and 325 sleeping bags.
s 85s
20
50
85(20) = 1700
85(50) = 4250
325 85(325) = 27,625
Holt Algebra 1

1-1 Variables and Expressions
Holt Algebra 1

1-1 Variables and Expressions
PRACTICE AND PROBLEM SOLVING, PAGES 9–11
17. the product of 5 and p; 5 groups of p
18. 4 decreased by y; the difference of 4 and y
19. the sum of 3 and x; 3 increased by x
20. the product of 3 and y; 3 times y
21. negative 3 times s; the product of negative 3 and s
22. the quotient of r and 5; one-fifth r
23. 14 decreased by t; the difference of 14 and t
24. the sum of x and 0.5; x increased by 0.5
25. t + 20
26. 8n
27. 6 - 5 = 1 28. 5 + 3 = 8
29. 6 ÷ 3 = 2 30. 5 · 6 = 30
31a. h - 40
b. h - 40
(40) - 40 = 0
(44) - 40 = 0
(48) - 40 = 0
(52) - 40 = 0
Holt Algebra 1

1-1 Variables and Expressions
32. To evaluate an expression is to find its value. To do this, substitute values for the variables and perform all the indicated operations.
33. 2x; possible answer: Jim has twice as many aunts
40.
x 10x
1 10(1) = 10 as Carly, who has x aunts.
34. 17 - b; possible answer: Sarah started with
17 apples, but lost b of them.
35. y + 10; possible answer; April had y CDs and then got 10 more.
36a. air pressure
b. depth below the water in feet.
c. 14.7 + 0.445d
= 14.7 + 0.445(8)
= 14.7 + 3.56
= 18.26 psi
38a. P = 2 + 2w b. P = 2 + 2w
= 2(14) + 2(8)
= 28 + 16
= 44 cm also contain variables.
TEST PREP, PAGE 11 and x.
5 10(5) = 50
10 10(10) = 100
15 10(15) = 150
44. Both algebraic and numerical expressions contain numbers and operations, but algebraic expressions
48. C; b fever than 3. 49. F; 12 - 5
50. B; Sarah’s has driven the difference of 25
CHALLENGE AND EXTEND, PAGE 11
51. 2ab = 2(6)(3)= 36
52. 2x + y = 2(4) + (5) = 13
c. A = · w or w d. A = w
= (8)(14)
= 112 cm 2
Holt Algebra 1

1-1 Variables and Expressions
SPIRAL REVIEW, PAGE 11
55. 180° - (45° + 90°) = 45°
56. 180° - (120° + 40°) = 40°
57. 180° - (30° + 60°) = 90°
58. 25% = 25/100 = 1/4
59. 50% = 50/100 = 1/2
60. 75% = 75/100= 3/4
61. 100% = 100/100= 1
62. add 8 to the previous term; 36, 44, 52
63. multiply the previous term by 3; 729, 2187, 6561
64. Add 1 to the previous term, then add 2, and then add 3, and so on; 17, 23, 30.
Holt Algebra 1