6.3.5 Translating words to algebraic expression

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

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

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

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

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

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

Answers p p 2z/ z/ m/2 6- m/2 (e-6) / 2 (e-6) / 2 5h + 2g 5h + 2g

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

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