There are two steps to solving math word problems:
Translate the wording into a numeric equation that
combines smaller "expressions"
Solve the equation!
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:
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:
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
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