1. Algebraic Representation
Unit 1 ~ Intro to Algebra
Algebraic Representation

2. Algebraic Representation
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". 

3. Algebraic Representation
The 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.

4. 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
fewer than*
reduced by
multiplied by of
product
times
double
triple
twice
divide
quotient
divided equally
per
ratio of
*be careful using “less than” and “fewer 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.

5. notice how the order changed
Examples . . .
verbal expression
algebraic expression
two more than a number
five less than three times a number
seven times a number, increased by 4
six decreased by 5 times a number
2 + x
3x – 5
notice how the order changed
7x + 4
6 – 5x

6. And in the other direction . . .
algebraic expression
verbal expression
2x - 4
Some possible 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