Algebraic Representation
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Solving problems in algebra depends on your ability to represent missing or unknown quantities.

Representing unknown quantities is easy to do
if you know the "language". 

For example, what operation is meant by the phrase more than ?


If you guessed addition, then you are right!  This skill of "translating" between words and mathematical operations just takes a little vocabulary drill.  Below are some of the most common phrases used in problem solving, together with the operations they represent.  Study these relationships and you should be a whiz at algebraic representation.
 

ADD

SUBTRACT

MULTIPLY

DIVIDE

add
sum
more than
increased by
exceeds
in all
total
gain
plus

subtract
difference
*less than
decreased by
diminished by
minus
fewer
reduced by
 

multiplied by
of
product
times
double
twice
triple

divide
quotient
divided equally
per
ratio of

* be careful using "less than" - it reverses the order of things
Also, be careful of the placement of commas in statements.
 In the statement "the sum of a and b, divided by 3" the comma indicates that
the answer is (a+b)/3 and not a + b/3.

 


Examples

 

1.   two more than a number

 

2 + x
 

2.   five less than three times a number

3x - 5
notice how this changed the order

3.   seven times a number, increased by 4

 

7x + 4

4.

  six decreased by 5 times a number

 

6 - 5x

 

Now let's try working in the other direction:

5.

Given 2x - 4, write a verbal expression that matches this mathematical expression.

Some possible verbal answers:
twice a number decreased by 4
four less than two times a value
double a number minus 4
two times a number diminished by 4