A mathematical expression involves adding, subtracting, multiplying, or dividing two or more terms. This is different from an equation, which involves an equals sign. You will either be asked to evaluate an expression given a value of a variable, or to simplify an expression.
It is important to remember the order of PEMDAS when evaluating expressions: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
You may be tested on your ability to evaluate expressions that involve exponents, absolute value, and general PEMDAS rules.
Absolute value, represented as a vertical line on either side of the value, refers to a number or variable’s distance from zero on the number line. There are always two numbers that share the same distance from zero: a positive number and its negative counterpart.
Thus, the absolute value of a number is that number without a positive or negative sign. For example:
|4| = 4
|-4| = 4
Both of these values (4 and -4) are equidistant from 0, and thus have the same absolute value.
You may have to evaluate an expression involving absolute value and variables. An expression such as |x| represents the distance the value x is away from zero. The expression |x - 4| represents the distance the value x is away from 4.
When evaluating expressions with large exponents, the exponent rules can be helpful to eliminate unnecessary calculations.
In a word problem, you are expected to construct and evaluate an expression based on the information provided to you.
Answers to Practice Problems