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 numberminus 4
two times a numberdiminished by 4