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1.6 Translating Word Phrases to Expressions 1. Translate word phrases to expressions. 2.5 Translating Word Sentences to Equations 1. Translate sentences to equations using key words, then solve. Copyright © 2011 Pearson Education, Inc. Translating Phrases Addition sum plus more than added to increased by Subtraction Multiplication minus subtracted from difference of less than decreased by less Order is important!! product twice times multiplied by of Division divided by quotient ratio divided into Order is important!! Translating Phrases Operation Addition Variable Expression Word Phrases x+3 Some number plus three Three added to some number The sum of some number and three Three more than some number Some number increased by three Translating Phrases Operation Subtraction Variable Expression Word Phrases y–6 Some number minus six Six subtracted from some number The difference of some number and six Six less than some number Some number decreased by six Some number less six Translating Phrases Operation Multiplication Exponents Roots Variable Expression Word Phrases 2a Twice some number Two times some number The product of two and some number Some number multiplied by two c2 c squared The square of c c to the second power k3 k cubed k to the third power The cube of k x The square root of x Translating Phrases Operation Division Variable Expression x 5 Word Phrases Some number divided by five The quotient of some number and five The ratio of some number and five Five divided into some number Translating Phrases The key words sum, difference, product, and quotient indicate the answer for their respective operations. sum of x and 3 x+3 difference of x and 3 x–3 product of x and 3 quotient of x and 3 x 3 or 3x x x 3 or 3 Translating Phrases Use x for the variable if not specified. The product of a number and four 4x The sum of b cubed and seven b3 7 Seven added to the quotient of x and y x 7 y x y Translating Phrases Use x for the variable if not specified. A number subtracted from 8 8x Nine divided into a number x 9 Five more than two times a number 2x 5 2x or 2x 5 Translating Phrases Use x for the variable if not specified. ab Seven times the sum of a and b 7a b 5x The product of five and a number minus the sum of the number and two x 2 5x x 2 5x x 2 Translating Phrases Use x for the variable if not specified. ab The sum of a and b divided by the difference of a and b ab ab ab Translate the phrase to an algebraic expression. Twelve less than three times a number a) 3n + 12 b) 12 – 3n c) 3n – 12 d) 3n 12 1.6 Copyright © 2011 Pearson Education, Inc. Slide 1- 12 Translate the phrase to an algebraic expression. Twelve less than three times a number a) 3n + 12 b) 12 – 3n c) 3n – 12 d) 3n 12 1.6 Copyright © 2011 Pearson Education, Inc. Slide 1- 13 Translate the phrase to an algebraic expression. The difference of a and b decreased by the sum of w and z a) (a – b) – (w + z) b) a – b – (w + z) c) ab – (w + z) d) (b – a) – (w + z) 1.6 Copyright © 2011 Pearson Education, Inc. Slide 1- 14 Translate the phrase to an algebraic expression. The difference of a and b decreased by the sum of w and z a) (a – b) – (w + z) b) a – b – (w + z) c) ab – (w + z) d) (b – a) – (w + z) 1.6 Copyright © 2011 Pearson Education, Inc. Slide 1- 15 Translating Word Sentences Operation Equals Expression = Word Phrases is is equal to is the same as produces yields results in Translate and Solve = Fifteen more than a number is negative seven. 15 x 15 x 7 15 15 x 22 7 Translate and Solve 13 4 x 4x Thirteen more than the product of four and a number yields 9. = 13 4 x 9 13 13 4 x 4 4 4 x 1 Translate and Solve 3 x 5 x5 Three times the difference of a number and five is equal to seven times the number, minus twelve. 7x = 7x 12 3 x 5 7 x 12 3x 15 7x 12 7x 7x 4 x 15 12 15 15 4x 3 4 4 3 x 4 Translate: Thirty-two less than three times a number is fifteen. a) 32 – 3x = 15 b) 3x – 32 = 15 c) 32 + 3x = 15 d) 3x 32 = 15 2.5 Translate: Thirty-two less than three times a number is fifteen. a) 32 – 3x = 15 b) 3x – 32 = 15 c) 32 + 3x = 15 d) 3x 32 = 15 2.5 Translate: The quotient of four less than a number and five is the same as the number divided by eight. a) 4 n 8n 5 b) 5(n 4) 8n 5 8 c) n4 n d) n 4 n 5 2.5 8 Translate: The quotient of four less than a number and five is the same as the number divided by eight. a) 4 n 8n 5 b) 5(n 4) 8n 5 8 c) n4 n d) n 4 n 5 2.5 8