Summary: Review

Key Concepts

Order of Operations

  1. Evaluate expressions within grouping symbols, [latex]( \ ), [ \ ] \ \mathrm{and} \ \{ \ \}[/latex]. Fractions have implied grouping of terms in the numerator and terms in the denominator.
  2. Evaluate exponents and radicals (such as square roots). Expressions under a radical have an implied grouping.
  3. Multiply and divide, left to right.
  4. 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