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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.**Vocabulary**variable constant numerical expression algebraic expression evaluate**A variable is a _____ or a ______ used to represent a value**that can change. A constant is a value that does not ______. A numerical expressioncontains only _______ and __________. An algebraic expression may contain _________, _________, and ________.**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, factors**Writing Math**These expressions all mean “2 times y”: 2y 2(y) 2•y (2)(y) 2 x y (2)y**Example 1: Translating from Algebra to Words**Give two ways to write each algebra expression in words. A. 9 + r B. q – 3 the difference of q and 3 the sum of 9 and r 9 increased by r 3 less than q C. 7mD. j 6 the product of m and 7 the quotient of j and 6 m times 7 j divided by 6**Check It Out! Example 1**Give two ways to write each algebra expression in words. 1b. 1a. 4 - n 1c. 9 + q 1d. 3(h)**To translate words into algebraic expressions, look for**words that indicate the action that is taking place. Put together, combine Find how much more or less Separate into equal groups Put together equal groups**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. m represents the number of minutes that John types. Think: m groups of 62 words 62 · m or 62m**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 represents Emily’s age. y + 4 Think: “older than” means “greater than.”**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. d represents the total amount that Joey will earn. Think: How many groups of $5 are in 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.**Check It Out! Example 2b**Miriam is 5 cm taller than her sister, than her sister who is m centimeters tall. Write an expression for Miriam’s height in centimeters.**Check It Out! Example 2c**Elaine earns $32 per day. Write an expression for the amount she earns in d days.**To evaluatean expression is to find its value.**To evaluate an algebraic expression, substitute numbers for the variables in the expression and then simplify the expression.**Example 3: Evaluating Algebraic Expression**Evaluate each expression for a = 4, b =7, and c = 2. A. b – c b – c = 7 – 2 Substitute 7 for b and 2 for c. Simplify. = 5 B. ac Substitute 4 for a and 2 for c. ac = 4 ·2 = 8 Simplify.**Check It Out! Example 3**Evaluate each expression for m = 3, n = 2, and p = 9. a.mn b. p – n c. p ÷ m**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. The expression 85s models the number of bottles to make s sleeping bags.**Example 4b: Recycling Application Continued**Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Find the number of bottles needed to make 20, 50, and 325 sleeping bags. Evaluate 85s for s = 20, 50, and 325. To make 20 sleeping bags 1700 bottles are needed. 85(20) = 1700 To make 50 sleeping bags 4250 bottles are needed. 85(50) = 4250 To make 325 sleeping bags 27,625 bottles are needed. 85(325) = 27,625**Writing Math**A replacement set is a set of numbers that can be substituted for a variable. The replacement set in Example 4 is (20, 50, and 325).**Check It Out! Example 4a**To make one sweater, 63 twenty ounce plastic drink bottles must be recycled. Write an expression for the number of bottles needed to make s sweaters.**Check It Out! Example 4b Continued**To make one sweater, 63 twenty ounce plastic drink bottles must be recycled. Find the number of bottles needed to make 12, 25 and 50 sweaters. Evaluate 63s for s = 12, 25, and 50. To make 12 sweaters 756 bottles are needed. 63(12) = 756 To make 25 sweaters 1575 bottles are needed. 63(25) = 1575 To make 50 sweaters 3150 bottles are needed. 63(50) = 3150**Lesson Quiz: Part I**Give two ways to write each algebraic expression in words. 1. j – 3 2. 4p 3. Mark is 5 years older than Juan, who is y years old. Write an expression for Mark’s age.**d**e Lesson Quiz: Part II Evaluate each expression for c = 6, d = 5, and e = 10. 4. 5.c + d Shemika practices basketball for 2 hours each day. 6. Write an expression for the number of hours she practices in d days. 7. Find the number of hours she practices in 5, 12, and 20 days.