Translating Verbal Phrases

Jennifer Duggan

\Verbal Phrases/Operation

Addition: The sum of a number and 8 x 8Five is added to a number x 5Two more than a number x 2A number increased by 3 x 3Subtraction: Four is subtracted from a number x 4Three less than a number x 3The difference between 7 and a number 7 xA number decreased by 2 x 2Multiplication: The product of 5 and a number 5xTwice a number 2xOne-half of a number xFive percent of a number 0.05xDivision: The ratio of a number to 6The quotient of 5 and a numberThree divided by some number.

There is often more than one unknown quantity in a problem, but arelationship between the unknown quantities is given. For example, if oneunknown number is 5more than another unknown number, we can usex and x  5,to represent them. Note that x and x  5 can also be used to represent twounknownnumbers that differ by 5, for if two numbers differ by 5, one of the numbersis 5more than the other.How would you represent two numbers that have a sum of 10? If one ofthenumbers is 2, the other is certainly 10 ­ 2, or 8. Thus if x is one of the

numbers,then 10 ­ x is the other. The expressionsx and 10 ­ xhave a sum of 10 for any value of x.

Verbal Phrase Algebraic Language 4 more than x x + 4 8 less than m m - 8 the product of 5 and x 5x y divided by 6 y/6 two times z increased by x 2z + x 4 times y, decreased by 3 times x 4y - 3x the sum of 6 times x, and 7 6x + 7

All of the examples involved translating a verbal phraseinto an algebraic expression.

It is also important to be able to translate a verbal sentence into analgebraic equation.

Let's look at a few of those examples....Five times a number y increased by 3, is 23.

5y + 3 = 2317 diminished by twice a number x is 1.

17 - 2x = 1The quotient of sixteen and x is 8

16/x = 8If five is increased by the product of three and x,

the result is 265 + 3x = 26

If a number y is added to three times ythe result is thirty-six.

3y + y = 36