Math101 · Independent Ontario learning library
Math101Evaluating Expressions
To evaluate an expression is to find its value for specified variable inputs. Evaluation replaces each variable consistently, preserves grouping, and then applies the order of operations.
Evaluation turns formulas and models into predictions. Careful substitution connects arithmetic to algebra and prepares learners for tables, functions, and scientific calculations.
Intuition and core definition
To evaluate an expression is to find its value for specified variable inputs. Evaluation replaces each variable consistently, preserves grouping, and then applies the order of operations. It does not solve for the variable because the variable values are already given.
Notation, language, and conditions
Function notation $f(3)$ means evaluate $f(x)$ at $x=3$. Substitution should use parentheses, especially for negative or fractional inputs: if $x=-2$, then $x^2=(-2)^2=4$. An expression has no equals sign until it is assigned a value or defined as part of an equation.
Why this idea matters
Evaluation replaces variables with specified values while preserving grouping, signs, and operation order so the expression keeps its intended structure.
A dependable method
- Record every given variable value and check the expression’s domain.
- Replace every occurrence of each variable with a parenthesized value.
- Evaluate grouping and exponents before multiplication, division, addition, and subtraction.
- Keep exact fractions or radicals unless approximation is requested.
- Estimate or use a second substitution layout to check the result.
