Kiosk Guides for Learning

Each problem that I solved became a rule
which served afterwards to solve other problems..
Brian Baxter,
American bookseller

Techniques in studying science and math menu

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 |
Evaluating algebraic expressions (PEMDAS) | Creating and developing spreadsheets |

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