Common textbook problems ask students to write an algebraic expression to resemble a verbal expression. For instance, "eight less than a number" translates to n-8. Algebraic expressions are a concise way to write lengthy verbal expressions. The following are a few more examples.
The sum of seven times a number and 3.
7x + 3
The product of two and the sum of a number and 9.
2(x + 9)
Twelve more than the quotient of a number and nine.
x/9 + 12
The quotient of a number and the sum of twelve and nine.
x/(12 + 9)
When writing an algebraic expression, make sure to read the verbal statement carefully. Most mistakes are caused by trying to get the problems done quickly.
An expression can be thought of as just a bunch of mathematical symbols, put together in a way that makes sense according to the rules of mathematics. For example, the following are expressions:
5 + 10
8 * (11 + 4) / 3 - 5
As stated above, an expression must follow the rules of mathematics. For example, the following is NOT an expression: 4 *+--54(
A variable can be thought of as something that holds the place of something else. Variables will commonly be denoted by the letters x, y.
An expression with a variable is just an expression that has a variable in it. The following are examples of expressions with variables:
4x - 8y
8x^2 + 3x - 5
x / y