 Intro
Before this page, the reader should have 
 Two Numbers  One Operation: Addition & Subtraction
This passage presents words related to each of the basic operations.
the reader should already be familiar with these words but, links have been provided in case a review is
desired.
Here are words associated with addition or subtraction. The context
is the key to the symbols needed, not the word itself. Examples follow the list.
words 
algebraic symbols  reason 
two decreased by a number  2  x  start with 2, make it smaller 
a number decreased by two  x  2  start with a number, make it smaller 
two less than a number  x  2  start with a number, make it smaller 
four more than a number  x + 4 or 4 + x  start with a number, add 4 
the difference between 6 and a number  6  x  subtract, starting with 6 
subtract four from a number  x  4  starting with a number, subtract 4 
the sum of 4 and a number  x + 4 or 4 + x  add to get a sum 
the opposite of the sum of a number and three 
(x+3) or (3+x)  take sum, take opposite
of sum 
It may be convenient for the reader to use the technique the author
used in writing the reason column.
 Think of the word expression as a task to be completed by a computation.
 Determine the operations needed.
 Think how one would start and, then
 think of what would need to be done to complete the task described.
Notice the uses of the
preposition "of" in the last example. Prepositional phrases break up the expressions into pieces.
Those beginning with "of" are discussed on the last page.
Below, notice how the prepositional phrases, in blue,
which begin with by, between, from, and than, make it easier to examine the phrase and determine
where to start and what to do.

words 
algebraic symbols  reason 
two decreased by a number 
2  x  start with 2, make it smaller 
a number decreased by two 
x  2  start with a number, make it smaller 
two less than a number 
x  2  start with a number, make it smaller 
four more than a number 
x + 4 or 4 + x  start with a number, add 4 
the difference between 6 and a number 
6  x  subtract, starting with 6 
subtract four from a number 
x  4  starting with a number, subtract 4 
the sum of 4 and a number 
x + 4 or 4 + x  add to get a sum 
the opposite of the sum of a number and three 
(x+3) or (3+x)  take sum, take opposite
of sum 
Additional information is found in a prepositional phrases. The
preposition "from" is almost always a tipoff that subtraction is required. Often, the desired
mathematical expression starts with what is in the "from" prepositional phrase. 
 Multiplication & Division
Here are words associated with multiplication or division.
The context is the key to the symbols needed, not the word itself. Remember,
the word AND is a signal that there are two or more ideas,
not that addition is required. Remember, to
use prepositional and other phrases to break up the expression in
order to determine what is required.
Examples follow the list.
words 
algebraic symbols  reason 
the product of two and a number  2x or 2(x) 
multiply 
a third of the sum of a number and two  (x + 2)/3 
start with the sum, take a third of it 
double the difference between 6 and a number 
2(6x)  start with the difference, multiply by 2 
triple the sum of four, five, and a number 
3(4 + 5 + x)  start with the sum, multiply by 3 
the value of 4 nickels 
4(5) or 5+5+5+5, etc.  four fives or five four times 
the value of some nickels 
5x  multiply 5 times a number 

The last example may be HARD. Use the table below to
examine the reason more clearly. The value of x nickels is 5x. The value of some nickels is 5x.

number of nickels  value of nickels 
1  5(1) = 5 
2  5(2) = 10 
3  5(3) = 15 
4  5(4) = 20 
x  5(x) = 5x 
 Exercises
 I. Write the expression/equation then check the answer.
 Note: Your browser may print the answers with spaces that are not ment to be there.
 1.) the square of five
 2.) the square of five subtracted from a number
 3.) the opposite of a number
 4.) six less than half of a number
 5.) the product of a number and four
 6.) a number decreased by five
 7.) five less than a number
 8.) Ten is five less than a number.
 9.) A number is less than five.
 See
additional info on these.
 10.) one less than a number
 11.) one less than a double a number
 12.) the opposite of the sum of a number and 12
 13.) triple a number
 14.) twice the sum of a number and 1

 III. Complete the table. Check each answer.
words 
algebraic symbols 
1.  x  1 
2. the sum of six and double a number  
3. double the sum of six and a number  
4. the sum of three consecutive integers 

5. the product of 2 consecutive odd integers 
 
 IV. Complete the table. Check each answer.
words  algebraic symbols 
1. one more than a number 

2.  x  1 
3. the product of a number and 3 and a different number  
4.  2x 
5.  x^{2}

