Transcript Holt Algebra 1 1-1

1-1 Variables and Expressions
Objectives
Translate between words and algebra.
Evaluate algebraic expressions.
Holt Algebra 1
1-1 Variables and Expressions
A variable is a letter used to represent a
value that can change.
2x  9
A constant is a value that does not change.
2x  9
A numerical expression contains only
constants and operations.
An algebraic expression may contain
variables, constants, and operations.
Holt Algebra 1
29
2x  9
1-1 Variables and Expressions
You will need to translate between algebraic
expressions and words to be successful in
math.
+
–
Plus, sum,
increased by
Minus, difference,
less than


Times, product
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Divided by,
quotient
1-1 Variables and Expressions
Writing Math
These expressions all mean “2 times y”:
2y
2(y)
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.
1a. 4 - n
4 decreased by n
n less than 4
1c. 9 + q
the sum of 9 and q
q added to 9
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1b.
the quotient of t and 5
t divided by 5
1d. 3(h)
the product of 3 and h
3 times h
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.
62m
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
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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.
5c  d
5 5
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d
c
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.
65t
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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2 5
B. ac
4 2  8
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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.
85s
Holt Algebra 1
1-1 Variables and Expressions
85s
Evaluate
Find the number of bottles needed to make
20, 50, and 325 sleeping bags.
s
85s
20
85(20) = 1700
50
85(50) = 4250
325
85(325) = 27,625
Holt Algebra 1
1-1 Variables and Expressions
Pages 9-11/17  35 Odd,36,38, 40,
44, 48  51,56  64 Even
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
40.
this, substitute values for the variables and perform
x 10x
all the indicated operations.
1 10(1) = 10
33. 2x; possible answer: Jim has twice as many aunts
5 10(5) = 50
as Carly, who has x aunts.
10 10(10) = 100
34. 17 - b; possible answer: Sarah started with
15 10(15) = 150
17 apples, but lost b of them.
35. y + 10; possible answer; April had y CDs and then
got 10 more.
44. Both algebraic and numerical expressions contain
36a. air pressure
numbers and operations, but algebraic expressions
b. depth below the water in feet.
also contain variables.
c. 14.7 + 0.445d
TEST PREP, PAGE 11
= 14.7 + 0.445(8)
48. C; b fever than 3. 49. F; 12 - 5
= 14.7 + 3.56
50. B; Sarah’s has driven the difference of 25
= 18.26 psi
and x.
38a. P = 2 + 2w b. P = 2 + 2w
CHALLENGE AND EXTEND, PAGE 11
= 2(14) + 2(8)
51. 2ab = 2(6)(3)= 36
= 28 + 16
52. 2x + y = 2(4) + (5) = 13
= 44 cm
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