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”.
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.
* 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 |