Kiosk Guides for Learning

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

# 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!

Suggestions:

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
• Draw and label all graphs and pictures clearly
• Note or explain each step of your process;
• 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 ofAlphie 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 pizzaswas 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: 3y I drive my car at 55 miles per hour.How far will I go in "x" hours? 55x 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 apartmentfor \$ "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.
• "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 thetotal 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 exams | Solving linear equations | Solving math word problems, introduction | Evaluating algebraic expressions (PEMDAS) | Creating and developing spreadsheets |

This guide has been adapted from
Purplemath (http://www.purplemath.com/index.htm) web site,
with permission of the author, Elizabeth Stapel ©2000-2001.