Translating Word Problems
Word List:
Addition
Add
Sum
*More than
Total
Increased by
Subtraction
Subtract
Difference
Less
*Less than
Decreased by
Minus
*Subtracted from
Exponent(Power)
Squared (2nd power)
Cubed (3rd power)
Fourth power (4th power)
Multiplication
Multiply
Product
Times
% of
(1/2, 2/3, etc.)of
Twice (2 x _)
Tripled (3 x _)
PER
Unknowns.
a number
what
Division
Equals
Divide
Equals
Quotient
is
pieces
are
ratio
was
separated the same as
equal parts represents
amounts to
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.
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.
Examples:
1. Five times three is fifteen.
translation:
5
x
3
= 15
2.
translation:
OR:
Twelve decreased by twice a number is six
12
–
2(
a ) = 6
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 )
15
Translating Word Problems
“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
correct translation :
5
x
2
(x 5 2, makes no sense)
“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.
1
“15% of x” means .15x or “half of x” means x
2
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)
16