Each problem that I solved became a rule
which served afterwards to solve other problems..
Solving math word problems
There are two steps to solving math word problems:
- Translate the wording into a numeric equation
that combines smaller "expressions"
- 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
|x + 2|
Express the total weight of
|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
|x - 6|
What is the
difference of my weight (x)
|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.
I drive my car at 55 miles per hour.
|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|
students rent an apartment
|x/3 or x ÷ 3|
cost a total of $25.00.
|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|
nine less than the
|(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|