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6.3.5 Translating words to algebraic expression

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Algebraic Expressions Expressions that contain at least one variable PROBLEM: Twice a number decreased by seven

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Keywords Refer to previously learned keywords for adding, subtracting, multiplying, and dividing SumHalf DifferenceLess than ProductMore than QuotientSubtracted from

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Rules Read each problem the way you read a book Read each problem the way you read a book Underline keywords and numbers Underline keywords and numbers “more than” or “less than” means flip the problem “more than” or “less than” means flip the problem

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Examples 3 less than a number n 3 less than a number n 5 more than p 5 more than p product of 7 and y product of 7 and y

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Translate into an algebraic expression Two times the sum of m and 8 2(m+8)

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Examples One more than the product of 12 and a number p One more than the product of 12 and a number p 4 less than the quotient of double z and 3 4 less than the quotient of double z and 3 Six minus the quotient of m and 2 Six minus the quotient of m and 2 Subtract 6 from e. Then, divide by 2. Subtract 6 from e. Then, divide by 2. The sum of five times h and twice g The sum of five times h and twice g

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Answers 1 + 12p 1 + 12p 2z/3 - 4 2z/3 - 4 6- m/2 6- m/2 (e-6) / 2 (e-6) / 2 5h + 2g 5h + 2g

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4 times a number cubed decreased by 7 4 times a number cubed decreased by 7 the quotient of nine less than x and twice x the quotient of nine less than x and twice x 15 less than a number squared 15 less than a number squared three plus the sum of the squares of w and x three plus the sum of the squares of w and x One-fourth the sum of r and ten is identical to r minus 4 One-fourth the sum of r and ten is identical to r minus 4

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Answers 4n 3 – 7 4n 3 – 7 (x-9) / (2x) (x-9) / (2x) N 2 – 15 N 2 – 15 3 + w 2 + x 2 3 + w 2 + x 2 ¼ (r+10) = r - 4 ¼ (r+10) = r - 4

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