Translating Word Problems
Word List:
Addition Subtraction Multiplication Division Equals
Add Subtract Multiply Divide Equals
Sum Difference Product Quotient is
*More than Less Times pieces are
Total *Less than % of ratio was
Increased by Decreased by (1/2, 2/3, etc.)of separated the same as
Minus Twice (2 x _) equal parts represents
*Subtracted from Tripled (3 x _) amounts to
PER
Exponent(Power) Unknowns.
Squared (2nd power) a number
Cubed (3rd power) what
Fourth power (4th power)
Note: Feel free to add more words to these lists as you find them. This is only a list of the more common words and is not meant to be complete.
Examples:
1. Five times three is fifteen.
translation: 5 x 3 = 15
2. Twelve decreased by twice a number is six
translation: 12 – 2 ( a ) = 6
OR: 12 – 2 ( a = 6
* note: 2(a) is the normal way to write multiplication in a word problem
(this means 2 times a, where “a” is some unknown number.)
3. Three plus five minus four multiplied by three squared
translation: 3 + 5 – 4 ( 32 )
“Out of order” problems: There are different types of problems that will be
“out of order” if you do a direct translation from words into math symbols.
Here are some of the more common types.
I. “Out of order-keywords” *Less than, *Subtracted from and *More than: These statements have asterisks next to them in the word list to remind you to reverse the numbers on either side of these statements.
Example:
Five less than thirteen is 8
direct translation: 5 – 13 = 8 (incorrect: 5 – 13 = -8, not 8)
correct translation : 13 – 5 = 8
Five subtracted from twenty-three is eighteen
direct translation: 5 – 23 = 18 (incorrect: 5 – 23 = -18, not +18)
correct translation : 23 – 5 = 18
Four more than Eight is Twelve
direct translation: 4 + 8 = 12
correct translation : 8 + 4 = 12
(This one actually works in either direction, but technically you are supposed to reverse it.) *On a multiple choice test the first one would be incorrect*
“Out of Order-sentences” Many times the operation is written first, followed
by the two numbers the operation is supposed to be applied to.
Just place the operation between the two numbers.
Hint: the word “and” is the spot the misplaced operation belongs in.
Think of it as a “target”
Example:
Operation First: The difference between eight and three
direct translation: – 8 3 (– 8 3, makes no sense)
correct translation : 8 – 3 (write the operation between the numbers)
Operation First: The product of five and two
direct translation: x 5 2 (x 5 2, makes no sense)
correct translation : 5 x 2
“Special Cases” Example:
The word “of”in word problems usually means nothing, unless there is a percent or a fraction in front of it” then it means to multiply.
“15% of x” means .15x or “half of x” means [pic]
Examples: 1. Four-fifths of eight 2. Twenty percent of four dollars
translation : 4/5 x 8 20% x $4
change percent to a decimal to work this one: (.20) (4)
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Steps for Translation Word Problems
I. Find all the numbers and variables (unknowns) in the problem, write them down above (or below) the word. (If it is already written in the form of a number, write it down again. If it is written in word form, change it into numerical form.)
II. Identify all Math Operation Words (given in the list above, write the symbol above/below the word(s) in the sentence.)
III. If there are any “out of order”or “special case” operations, write them in the correct order.
Note: If there are any “unknowns” use a letter (like x, y, a, b…) to represent that word.
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