Unit 1 Intro to Algebra Algebraic Representation Solving

Unit 1 ~ Intro to Algebra

Algebraic Representation Solving problems in algebra depends on your ability to represent missing or unknown quantities. Representing unknown quantities is easy to do if you know the "language".

Algebraic Representation The skill of "translating" between words and mathematical operations just takes a little vocabulary drill. Below are some of the most common phrases used in problem solving, together with the operations they represent. Study these relationships and you should be a whiz at algebraic representation.

Algebraic Representation Add Subtract Multiply Divide add sum more than increased by exceeds in all total gain plus subtract difference less than* decreased by diminished by minus fewer than* reduced by multiplied by of product times double triple twice divide quotient divided equally per ratio of *be careful using “less than” and “fewer than” – it reverses the order of things! Also, be careful of the placement of commas in statements. In the statement “the sum of a and b, divided by 3” the comma indicates that the answer is (a + b)/3 and not a + b/3.

Examples. . . verbal expression algebraic expression two more than a number 2+x five less than three times 3 x – 5 a number notice how the order changed seven times a number, increased by 4 7 x + 4 six decreased by 5 times a number 6 – 5 x

And in the other direction. . . algebraic expression verbal expression Some possible answers: 2 x - 4 • twice a number decreased by 4 • four less than two times a value • double a number minus 4 • two times a number diminished by 4