Translating Words Into Mathematical Symbols
Before we begin solving word problems, we need to be very comfortable with translating words into mathematical symbols. Following is a partial list of words and their mathematical equivalents.
Concept 
Symbol 
Words 
Example 
Translation 
equality 
= 
is 
2 plus 2 is 4 
2 + 2 = 4 


equals 
x minus 5 equals 2 
x – 5 = 2 


is the same as 
multiplying x by 2 is the same as dividing x by 7 
2x = x/7 
addition 
+ 
sum 
the sum of y and π is 20 
y + π = 20 


plus 
x plus y equals 5 
x + y = 5 


add 
how many marbles must John add to collection P so that he has 13 marbles 
x + P = 13 


increase 
a number is increased by 10% 
x + 10%x 


more 
the perimeter of the square is 3 more than the area 
P = 3 + A 
subtraction 
– 
minus 
x minus y 
x – y 


difference 
the difference of x and y is 8 
x – y = 8 


subtracted 
x subtracted from y 
y – x 


less than 
the circumference is 5 less than the area 
C = A – 5 
multiplication 
× or • 
times 
the acceleration is 5 times the velocity 
a = 5v 


product 
the product of two consecutive integers 
x(x + 1) 


of 
x is 125% of y 
x = 125%y 
division 
÷ 
quotient 
the quotient of x and y is 9 
x ÷ y = 9 


divided 
if x is divided by y, the result is 4 
x ÷ y = 4 
Although exact steps for solving word problems cannot be given, the following guidelines will help:
 First, choose a variable to stand for the least unknown quantity, and then try to write the other unknown quantities in terms of that variable.
 Second, write an equation that involves the expressions in Step 1. Most (though not all) word problems pivot on the fact that two quantities in the problem are equal. Deciding which two quantities should be set equal is usually the hardest part in solving a word problem since it can require considerable ingenuity to discover which expressions are equal.
 Third, solve the equation in Step 2 and interpret the result.
For the example above, we would get by adding the x’s:

3x – 5 = 16

Then adding 5 to both sides gives

3x = 21

Finally, dividing by 3 gives

x = 7
