Translating Phrases to Mathematical Expressions

Translating Phrases to Mathematical Expressions

Many words and phrases suggest mathematical operations. The following common words and phrases indicate addition, subtraction, multiplication, and division:

 Addition Subtraction Multiplication Division plusthe sum ofincreased bytotalmore thanadded to minusthe difference ofdecreased byfewer thanless thansubtracted from timesthe product ofmultiplied byof divided bythe quotient ofper

Verbal phrases can be translated into variable expressions.  Some examples are below.

 Verbal Phrase Variable Expression The sum of a number and 9 n + 9 The difference of a number and 21 n − 21 The product of 6 and a number 6n The quotient of 48 and a number One third of a number

Whenever possible, select a single variable to represent an unknown quantity. Then express related quantities in terms of the first variable selected.

Examples

For each relationship, select a variable to represent one quantity and state what that variable represents. Then express the second quantity in terms of the variable selected.

a) The Kings scored 7 more points than the Rangers.

Let r = number of points scored by the Rangers
Then r + 7 = number of points scored by the Kings

b) Bob and Marc share \$65.

Let a = how much Bob receives.
Then 65 − a = amount Marc receives.

Practice

Write each statement as an algebraic expression.

1)  Kim has 7 more than 5 times the amount Sylvia has.

2)  The length of a rectangle is 3 feet less than 4 times its width.

3)  Write an expression to represent how much a realtor will earn at a 6% commission on a house that costs x dollars.

Write each problem below as an equation.

4)  The number of cents in d dimes is 120.

5)  The cost of x gallons of gasoline at \$3.20 per gallon is \$35.20.

6)  One train travels 3 miles more than twice the distance another train travels.  The total distance traveled by both trains is 800 miles.

1)  s = the amount Sylvia has;  5s + 7 = the amount Kim has

2)  w = width of the rectangle;  4w − 3 = length of the rectangle

3)  0.06x

4)  10d = 120

5)  3.20x = 35.20

6)  x + (2x + 3) = 800