Key Concepts
Order of Operations
- Evaluate expressions within grouping symbols, [latex]( \ ), [ \ ] \ \mathrm{and} \ \{ \ \}[/latex]. Fractions have implied grouping of terms in the numerator and terms in the denominator.
- Evaluate exponents and radicals (such as square roots). Expressions under a radical have an implied grouping.
- Multiply and divide, left to right.
- Add and subtract, left to right.
Translating Verbal Statements Involving Inequalities to Mathematical Statements
| Verbal statement k is … |
Mathematical Statement |
| greater than or equal to k at least k not less than k |
[latex]x \geq k[/latex] |
| less than or equal to k at most k not more than k |
[latex]x \leq k[/latex] |
| less than k below k fewer than k |
[latex]x < k[/latex] |
| greater than k more than k above k |
[latex]x > k[/latex] |
| equal to k is k exactly k the same as k |
[latex]x=k[/latex] |
| not equal to k not k different from k |
[latex]x \neq k[/latex] |
Glossary
- Algebraic expression: an expression involving addition, subtraction, multiplication, division, and exponentiation by a rational exponent
- Complex fraction: a fraction that contains fractions in the numerator and/or the denominator
- Secondary fraction: a fraction in the numerator or denominator of a complex fraction
