Holt Algebra 1

1-1 Variables and Expressions

Translate between words and algebra. Evaluate algebraic expressions.

Objectives

Holt Algebra 1

1-1 Variables and 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 expression contains only constants and operations.

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

2 9x

2 9x

2 9

2 9x

Holt Algebra 1

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 Divided by,quotient

Holt Algebra 1

1-1 Variables and Expressions

These expressions all mean “2 times y”:2y 2(y)2•y (2)(y)2 y (2)y

Writing Math

Holt Algebra 1

1-1 Variables and Expressions

1a. 4 - n 1b.

1c. 9 + q 1d. 3(h)

4 decreased by n

the sum of 9 and q

the quotient of t and 5

the product of 3 and h

Give two ways to write each algebra expression in words.

Check It Out! Example 1

n less than 4 t divided by 5

q added to 9 3 times h

Holt Algebra 1

1-1 Variables and Expressions

John types 62 words per minute. Write an expression for the number of words he types in m minutes.

Example 2A: Translating from Words to Algebra

62m

Holt Algebra 1

1-1 Variables and Expressions

Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age

Example 2B: Translating from Words to Algebra

4y

Holt Algebra 1

1-1 Variables and Expressions

5c d5

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.

Example 2C: Translating from Words to Algebra

5 5cd

Holt Algebra 1

1-1 Variables and Expressions

Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours.

Check It Out! Example 2a

65t

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

Evaluate each expression for a = 4, b =7, andc = 2.

A. b – c

B. ac

Example 3: Evaluating Algebraic Expression

7 52

4 82

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.

85sWrite an expression for the number of bottles needed to make s sleeping bags.

Holt Algebra 1

1-1 Variables and Expressions

Find the number of bottles needed to make20, 50, and 325 sleeping bags.

s 85s

20

50

325

85(20) = 1700

85(50) = 4250

85(325) = 27,625

85s Evaluate

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 ExpressionsPRACTICE AND PROBLEM SOLVING, PAGES 9–1117. the product of 5 and p; 5 groups of p18. 4 decreased by y; the difference of 4 and y19. the sum of 3 and x; 3 increased by x20. the product of 3 and y; 3 times y21. negative 3 times s; the product of negative 3 and s22. the quotient of r and 5; one-fifth r23. 14 decreased by t; the difference of 14 and t24. the sum of x and 0.5; x increased by 0.525. t + 20 26. 8n27. 6 - 5 = 1 28. 5 + 3 = 829. 6 ÷ 3 = 2 30. 5 · 6 = 3031a. h - 40b. h - 40(40) - 40 = 0(44) - 40 = 0(48) - 40 = 0(52) - 40 = 0

Holt Algebra 1

1-1 Variables and Expressions32. To evaluate an expression is to find its value. To dothis, substitute values for the variables and performall the indicated operations.33. 2x; possible answer: Jim has twice as many auntsas Carly, who has x aunts.34. 17 - b; possible answer: Sarah started with17 apples, but lost b of them.35. y + 10; possible answer; April had y CDs and thengot 10 more.36a. air pressureb. depth below the water in feet.c. 14.7 + 0.445d= 14.7 + 0.445(8)= 14.7 + 3.56= 18.26 psi38a. P = 2 + 2w b. P = 2 + 2w= 2(14) + 2(8)= 28 + 16= 44 cmc. A = · w or w d. A = w= (8)(14)= 112 cm 2

40. x 10x1 10(1) = 105 10(5) = 5010 10(10) = 10015 10(15) = 150

44. Both algebraic and numerical expressions containnumbers and operations, but algebraic expressionsalso contain variables.

TEST PREP, PAGE 1148. C; b fever than 3. 49. F; 12 - 550. B; Sarah’s has driven the difference of 25

and x.CHALLENGE AND EXTEND, PAGE 1151. 2ab = 2(6)(3)= 3652. 2x + y = 2(4) + (5) = 13

Holt Algebra 1

1-1 Variables and ExpressionsSPIRAL REVIEW, PAGE 1155. 180° - (45° + 90°) = 45°56. 180° - (120° + 40°) = 40°57. 180° - (30° + 60°) = 90°58. 25% = 25/100 = 1/459. 50% = 50/100 = 1/260. 75% = 75/100= 3/461. 100% = 100/100= 162. add 8 to the previous term; 36, 44, 5263. multiply the previous term by 3; 729, 2187, 656164. Add 1 to the previous term, then add 2, and thenadd 3, and so on; 17, 23, 30.