There are two steps to solving math word
problems:
- Translate the wording into a numeric equation
that combines smaller "expressions"
- Solve the equation!
|
Math expressions
(examples): |
| addition: 5+x |
subtraction: 5-x |
| multiplication:
5*x; 5x |
division:
5
÷ x; 5/x |
Key words for addition
+
:
increased by; more than; combined together; total of;
sum; added to("mouse
over" the block for answer) |
|
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 children 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: |
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 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 |
Word problems are a series of expressions that fits into an equation
An equation is a combination of math expressions.
Suggestions:
- 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:
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 tanked up, I paid $3.90 for three gallons, so the gas
was 1.30 a gallon, or $1.30/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
=
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 |
|
|
|
Word problems for you to solve from: |
Purplemath |
"Age"
problems, involving figuring out how old people are (or will be)
"Area/volume/perimeter" problems, involving very basic geometric formulas
"Coin"
problems, involving figuring out how many of each type of coin you have
"Distance" problems,
involving speed/rate, distance, time, and the formula "d = rt".
"Investment" problems, involving investments, interest rates, and the
formula "I = Prt".
"Mixture" problems, involving combining elements and find prices (of the
mixure) or percentages (of, say, acid or salt).
"Number"
problems, involving "Three more than two times the smaller number..."
"Percent
of" problems, involving finding percents, increase/decrease, discounts,
etc.
"Work" problems, involving two or more people or things working together
to complete a task, and finding how long they took.
Related topics in the Purplemath web site:
canceling units,
percent of, solving equations.
Purplemath index of lessons: http://www.purplemath.com/modules/modules.htm
Also:
Ask Dr. Math: Middle School Word Problems
This guide has been adapted from
Purplemath (http://www.purplemath.com/index.htm)
web site, with permission of the author,
Elizabeth Stapel ©2000-2001.
Website overview: Since 1996 the
Study Guides and Strategies web site
has been researched, authored, maintained and supported by Joe Landsberger
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