Each problem that I solved
became a rule
which served afterwards
to solve other problems.
Rene Descartes
French 1596 - 1650
An equation is a combination of math expressions.
Word problems are a series of expressions
that fits into an equation
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:
* 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
o Draw and label all graphs and pictures clearly
o 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
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
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"
Examples: check your answer with a "mouse over"
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
* Test yourself on the keywords
* Exercise 1: Solving math word problems
* Exercise 2: Solving math word problems
* Resolving (algebraic) equations
Word problems for you to solve from:
Purplemath
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