Translating Expressions and Equations Examples

Translate the following verbal expression into a numeric expression: Ten less than the product of a number and 13.
The phrase "Ten less than" means 10 is being subtracted from something, so it's gotta go at the end. ___ – 10
What is 10 less than? It's less than a product, so we'll put some parentheses before the – 10. ( )( ) – 10
What is being multiplied in the product? A number (we'll call it n) and 13, so we put them in the parentheses. (13)(n) – 10
Drop the parentheses and the expression is 13n – 10, which is our final answer.

Which of the following is the best translation of the numeric expression 20(a + 6) – 18? a. Twenty less than eighteen times the sum of a number and six. b. Eighteen less than the sum of a number and six. c. The product of twenty and the sum of a number and six. d. Eighteen less than the product of twenty and the sum of a number and six.
Because 18 is being subtracted from the expression, the phrase "eighteen less than" needs to come at the beginning of the translation. Bam, that immediately eliminates answers a and c.
The expression begins with a product because we're multiplying 20 by something. So after the phrase "eighteen less than," we should have a product. That eliminates answer b.
Answer d is left, and it includes "eighteen less than" and "the product of twenty…" and "the sum of a number and six." It includes all three operations, and in the right order. We have a winner.

The sum of a number and seven is equal to forty-five. What is the number?
We first grab our handy Math-English Dictionary and translate the problem into numeric form. We know that we have a sum, so we're adding two things. Whip out a plus sign. +
We're adding some unknown number and seven. Let's use the variable x for the mystery number, then add seven to it. x + 7
The whole deal equals forty-five. x + 7 = 45 Now we've got an equation, so we're ready to solve for x.
Subtract 7 from both sides. x + 7 – 7 = 45 – 7 x = 38 You've been owned, equation.