
Algebraic Expressions:
Unlike equations, algebraic expressions do not contain an equal sign.

The word "terms" refers to values that are added or subtracted. 7n + 2 has two terms.
The word "factors" refers to values that are multiplied. The term 7n has two factors: 7 and n.

The skill of translating between verbal statements and algebraic expressions requires an understanding of the words that are commonly used to represent mathematical operations.
A sampling of words used to represent mathematical operations:
ADD 
SUBTRACT 
MULTIPLY 
DIVIDE 
add
sum
increased by
more than
exceeds
total
plus
in all
gain
deposit 
subtract
difference
decreased by
fewer
less than *
diminished by
minus
take away
withdraw
reduced by

multiply
product
of
times
double
triple
twice

divide
quotient
per
divided equally
split into
fraction
ratio of

* Remember that "less than" reverses the order of what you read. [ 6 less than x, becomes x  6 ]

Always look for the placement of commas in the verbal statements. They will help you decide how to properly group terms in your algebraic expression.
For example: the verbal statement
"5 times, a number increased by 6" translates to 5(n + 6) and is not 5n + 6.


(Remember that variables can be represented by any letter or symbol, unless otherwise directed.) 

Verbal Statement 
Algebraic Expression 
1. 
Five increased by four times a number 
5 + 4n 
2. 
Eight less than twice a number 
2n  8 
3. 
Three times a number, increased by 9 
3n + 9 
4. 
The product of 4, and a number decreased by 7 
4(n  7) 
5. 
The number of feet in x yards. 
3x 
6. 
Express the width of a rectangle which is seven less than its length, l. 
l  7 
7. 
A number repeated as a factor 3 times. 
n • n • n = n^{3} 
Terms used to refer to specific expressions:
TERM 
DESCRIPTION 
EXAMPLES 
monomial 
The product of nonnegative integer powers of variables. It has ONE term. (mono implies one) 
12, 3x, 2x^{2}, 7ab, 4t^{3}s^{4} 
binomial 
The sum of two monomials. It has TWO unlike terms. (bi implies two) 
7x + 4, x^{2} +1, 3a  2b 
trinomial 
The sum of three monomials. It has THREE unllike terms. (tri implies three) 
x^{2} + 4x + 4, 4p^{2}  3q^{3}  1 
polynomial 
A generic term for the sum of one or more monomials. (poly implies many) 
4x, s + 2, a^{2} + b^{2} + c 
Algebraic Equations:
Unlike expressions, algebraic equations contain an equal sign.
EQUAtion EQUAl sign
You will still encounter the "words" used to represent mathematical operations, as shown in the chart at the top of the page. To that list, we can now add a sampling of words that imply "an equal sign".
EQUAL 
is,
are, was, were, equivalent to, same as, yields, gives 
Also, continue to look for commas, to help you group your terms.

When trying to create equations, you may find it difficult to quickly arrive at an answer. When this happens, it is often helpful to make up a numerical example from the situation so you can see how the numbers are related to one another. In addition, a numerical example is useful for checking to see if the equation you wrote is accurate.




Verbal Statement 
Algebraic Equation 
1. 
Three times a number, divided by ten equals fifteen. 

2. 
Ten less than the quotient of a number and two is zero. 

3. 
Twelve more than the product of a number and two is thirtysix. 
2n + 12 = 36 
4. 
Represent the cost of access to a movie web site which charges a $5 fee for the first month, and then $28 a month for continued access after the first month.
Numerical Example: For 4 months the cost would be: Cost = $5 + $28•(41). Replace 4 with m for number of months. 
c = cost, m = months
c =
5 + 28(m  1) 
5. 
If chocolate doughnuts cost $1.10 and chocolate chip muffins cost $2.25, how many of each can you purchase for $20?
Numerical Example: The cost of 3 doughnuts and 2 muffins will be: Cost = $1.50•3 + $2.25• 2. Replace 3 with d for doughnuts, 2 with m for muffins, and Cost with $20.

d =doughnuts, m = muffins
20 =
1.50d + 2.25m 
6. 
Express the area of a rectangle whose length is twice its width decreased by 6.
Numerical Example: If the width is 10, the length is 14, then the area, A = 10 • 14. Just replace 10 with w for width, and 14 with 2w  6 for the length. 
A = area, w = width
A = w • (2w  6) 
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