1.4 Evaluating Expressions

Algebraic equations contain both numbers and variables. In this section, we will learn how to evaluate algebraic expressions when the values of the variables are given. 

 

A mathematical expression that consists of variables, numbers and algebraic operations is called an algebraic expression.

For example: $30x+20y$ and $5x^{3}y-2x{y}^2-z+4$ are algebraic expressions. 

Evaluate an algebraic expression means to find the value of the expression when the variables are substituted by certain numbers. 

For example: when $x=2$ and $y=3$, the value of the expression $30x+20y$ is $30\cdot 2+20\cdot 3=60$. 

 

Examples: Evaluate for $a=1$, $b=2$, $c=4$, and $d=-1$.

        $=-35$

 

Example: Find the area of a triangle with height of $20\mathrm{in}$ and a base of $30\mathrm{in}$.

The area is $A={\displaystyle \frac{1}{2}}\cdot b\cdot h={\displaystyle \frac{1}{2}}\cdot 20\mathrm{in}\cdot 30\mathrm{in}=300{\mathrm{in}}^2$.