Lesson 1: Evaluating Multi-Variable Expressions

Property

Substituting a specific value for a variable into an expression and calculating the result is called evaluating the expression. This process turns a general algebraic rule into a specific numerical answer.

Examples

• To evaluate the expression $4k - 1$ when $k = 3$, we substitute 3 for $k$: $4(3) - 1 = 12 - 1 = 11$.
• Find the value of $\frac{m}{5} + 2$ for $m = 20$. We calculate $\frac{20}{5} + 2 = 4 + 2 = 6$.
• If a taxi fare is $2d + 3$ where d is distance in miles, a 5-mile trip costs $2(5) + 3 = 10 + 3 = 13$ dollars.

Explanation

Evaluating an expression is like using a recipe. The expression is the general recipe, and the given value for the variable is the specific ingredient. You just plug in the number and do the math to find the final result.

Property

When evaluating expressions with multiple variables, substitute all given variable values simultaneously before applying order of operations: For expression $f(x,y,z)$ with given values $x = a$, $y = b$, $z = c$, replace all variables at once to get $f(a,b,c)$.

Examples