Addition add(ed) to all together both combined in all increase by more than perimeter plus sum total	Subtraction decreased by difference fewer than how many more left less less than minus remaining take away
Multiplication a area multiplied by of per product of rate times triple twice	Division divided  half how many each out of percent quarter quotient of percent

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:

• 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	y + 30

GAME