Your Study Guides and Strategies starts here!

Each problem that I solved
became a rule
which served afterwards
to solve other problems.
Rene Descartes 1596 - 1650
French philosopher

Math series

Solving math word problems

There are two steps to solving math word problems:

  1. Translate the wording into a numeric equation
    that combines smaller "expressions"
  2. Solve the equation!


  • Read the problem entirely
    Get a feel for the whole problem
  • List information and the variables you identify
    Attach units of measure to the variables (gallons, miles, inches, etc.)
  • Define what answer you need,
    as well as its units of measure
  • Work in an organized manner
    Working clearly will help you think clearly
    • Draw and label all graphs and pictures clearly
    • Note or explain each step of your process;
      this will help you track variables and remember their meanings
  • Look for the "key" words (above)
    Certain words indicate certain mathematical operations:

Math expressions (examples):
after you review the keywords, test yourself

addition: 5+x subtraction: 5-x
multiplication: 5*x; 5x division: 5 ÷ x; 5/x
Exercise: ("mouse over" the block for answer)
Key words for addition +
increased by; more than; combined together; total of; sum; added to

What is the sum of 8 and y?

8 + y

Express the number (x) of apples
increased by two

x + 2

Express the total weight of
Alphie the dog (x) and Cyrus the cat (y)

x + y
Key words for Subtraction -
less than, fewer than, reduced by, decreased by, difference of

What is four less than y

y - 4

What is nine less than a number (y)

y - 9

What if the number (x) of pizzas
was reduced by 6?

x - 6

What is the difference of my weight (x)
and your weight (y)

x - y
Key words for multiplication * x or integers next to each other (5y, xy):
of, times, multiplied by

What is y multiplied by 13

13y or 13 * y

Three runners averaged "y" minutes.
Express their total running time:


I drive my car at 55 miles per hour.
How far will I go in "x" hours?

Key words for division ÷ /
per, a; out of; ratio of, quotient of; percent (divide by 100)

What is the quotient of y and 3

y/3 or y ÷ 3

Three students rent an apartment
for $ "x" /month. What will each have to pay?

x/3 or x ÷ 3

"y" items cost a total of $25.00.
Express their average cost:

25/y or 25 ÷ y

More vocabulary and key words:

  • "Per" means "divided by"
    as "I drove 90 miles on three gallons of gas, so I got 30 miles per gallon."
    (Also 30 miles/gallon)
  • "a" sometimes means "divided by"
    as in "When I filled up, I paid $10.50 for three gallons of gasoline,
    so the gas was 3.50 a gallon, or $3.50/gallon
  • "less than"
    If you need to translate "1.5 less than x", the temptation is to write "1.5 - x". DON'T! Put a "real world" situation in, and you'll see how this is wrong: "He makes $1.50 an hour less than me." You do NOT figure his wage by subtracting your wage from $1.50.
    Instead, you subtract $1.50 from your wage
  • "quotient/ratio of" constructions
    If a problems says "the ratio of x and y",
    it means "x divided by y" or x/y or x ÷ y
  • "difference between/of" constructions
    If the problem says "the difference of x and y",
    it means "x - y"

What if the number (x) of children was reduced by six, and then they had to share twenty dollars? How much would each get?

20/(x - 6)

What is 9 more than y?

y + 9

What is the ratio of 9 more than y to y?

(y + 9)/y

What is nine less than the
total of a number (y) and two

(y + 2) - 9 or  y - 7

The length of a football field is 30 yards more than its width "y". Express the length of the field in terms of its width y

y + 30

Math series

Math exams | Solving linear equations | Solving math word problems, introduction |
Word problems, exercise I | Word problems, II | Word problems, III |
Evaluating algebraic expressions | Creating and developing spreadsheets |
P.E.M.D.A.S.: 2nd exercise | P.E.M.D.A.S.: 3rd exercise | Sudoku 数独

This guide has been adapted from
Purplemath ( web site,
with permission of the author, Elizabeth Stapel ©2000-2001.