Lesson 4: Evaluating Algebraic Expressions

Property

When we evaluate an algebraic expression, we follow the order of operations.
Order of Operations:

1. Perform any operations inside parentheses, or above or below a fraction bar.
2. Perform all multiplications and divisions from left to right.
3. Perform additions and subtractions from left to right.

Examples

• Evaluate $30 - 4x$ for $x=2$. Substitute: $30 - 4(2)$. Multiply: $30 - 8$. Finally, subtract: $22$.
• Evaluate $2(a + 1)$ for $a=5$. Substitute: $2(5+1)$. Add: $2(6)$. Finally, multiply: $12$.
• Evaluate $7(b + 3) + 5$ for $b=2$. Substitute: $7(2 + 3) + 5$. Add: $7(5) + 5$. Then, multiply: $35+5$. Finally, add: $40$.

Explanation

Evaluating an expression means finding its final numerical value. The Order of Operations is the universal rulebook that ensures everyone gets the same answer from the same calculation. Always follow the steps precisely.

Property

To evaluate a variable expression with fractions, substitute the given fraction for each variable in the expression. Then, use the order of operations (PEMDAS/BODMAS) to simplify the resulting numerical expression. This often involves adding, subtracting, multiplying, or dividing the fractions as needed.

Examples

• Evaluate $x + \frac{3}{5}$ when $x = \frac{4}{5}$. Substitute to get $\frac{4}{5} + \frac{3}{5} = \frac{4+3}{5} = -\frac{7}{5}$.
• Evaluate $3a^2b$ when $a=\frac{1}{2}$ and $b=\frac{1}{3}$. Substitute: $3(\frac{1}{2})^2(\frac{1}{3}) = 3(\frac{1}{4})(\frac{1}{3}) = \frac{3}{12} = \frac{1}{4}$.
• Evaluate $\frac{a+b}{c}$ when $a=\frac{1}{4}$, $b=\frac{3}{8}$, and $c=\frac{1}{2}$. Substitute to get $\frac{\frac{1}{4}+\frac{3}{8}}{\frac{1}{2}} = \frac{\frac{5}{8}}{\frac{1}{2}} = \frac{5}{4}$.

Explanation

This process combines algebra and fractions. Simply plug the given fraction values into the expression in place of the variables. After substituting, follow the order of operations to calculate the final answer, using your fraction arithmetic skills.

Property

To evaluate an algebraic expression with decimals, substitute the given value for the variable and simplify the expression using the order of operations.

Examples

• Evaluate $4.5x - 2.1$ for $x = 3$.

• Evaluate $\frac{z}{0.5} + 7.8$ for $z = 4.3$.