Translate between words and algebra. Evaluate algebraic expressions.

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Translate between words and algebra. Evaluate algebraic expressions.

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Translate between words and algebra. Evaluate algebraic expressions.

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Objectives

Translate between words and algebra.

Evaluate algebraic expressions.

A variable is a letter used to represent a value that can change.

A constant is a value that does not change.

A numerical expressioncontains only constants and operations.

An algebraic expression may contain variables, constants, and operations.

You will need to translate between algebraic expressions and words to be successful in math.

Plus, sum,

increased by

Minus, difference, less than

Divided by,

quotient

Times, product

Writing Math

These expressions all mean “2 times y”:

2y 2(y)

2•y (2)(y)

2 y (2)y

Check It Out! Example 1

Give two ways to write each algebra expression in words.

1b.

1a. 4 - n

4 decreased by n

the quotient of t and 5

n less than 4

t divided by 5

1c. 9 + q

1d. 3(h)

the sum of 9 and q

the product of 3 and h

3 times h

q added to 9

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.

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

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.

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.

To evaluatean expression is to find its value.

Substitute numbers for the variables and simplify.

Example 3: Evaluating Algebraic Expression

Evaluate each expression for a = 4, b =7, and

c = 2.

A. b – c

B. ac

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.

Find the number of bottles needed to make

20, 50, and 325 sleeping bags.

85(20) = 1700

85(50) = 4250

85(325) = 27,625

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

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

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

c. A = · w or w d. A = w

= (8)(14)

= 112 cm 2

40.

x 10x

1 10(1) = 10

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

also contain variables.

TEST PREP, PAGE 11

48. C; b fever than 3. 49. F; 12 - 5

50. B; Sarah’s has driven the difference of 25 and x.

CHALLENGE AND EXTEND, PAGE 11

51. 2ab = 2(6)(3)= 36

52. 2x + y = 2(4) + (5) = 13

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.