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 | ||
plus the sum of increased by total more than added to | minus the difference of decreased by fewer than less than subtracted from | times the product of multiplied by of | divided by the quotient of per |
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.
Answers
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