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  • Math series

     

    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
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Page Comments

• 
  Megan Reichert on 2009-03-13
  This resource would be very helpful to any math classroom. It give good examples of how a problem should be set up. It tells the user what to look for in order to determine how to set up the corresponding equation. It also give several examples where the user can tell themselves to see if they can look at a sentence and determine what type of equation it corresponds to. This little keyword triggers are very important for students in algebra to understand, and this website helps the user practice to test what they know and what they need to work on.

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