Evaluating Algebraic Expressions

LESSON OBJECTIVES

When you complete this lesson, you will be able to:

• Evaluate algebraic expressions
• Evaluate formulas and other expressions

LESSON SUMMARY

When we are asked to “evaluate” an algebraic expression, we are told which numbers the letters stand for. Then, to figure out the value of the entire expression, we simply replace each letter with the number it stands for. For example, suppose we are told to evaluate the algebraic expression 3M + P if M = 2 and P = 8. We replace M with 2 and P with 8, and complete the problem as shown below.

• 3M + P
• 3(2) + 8
• 6 + 8
• 14

Self-Test

Use this test to check your understanding.

Evaluate these algebraic expressions:

1. 7G – 5H, if G = 8, H = 6
2. \(\frac{4S\;+\;T^2}V\) if S = 7, T = 6, V = 8

Compare your answers with those below.

Answers to Self-Test

1. 26
2. 8

Examples

These examples can help you master the new ideas in this lesson.

Evaluate each of the following algebraic expressions:

1. 5v + y, if v = 3, y = 2.
2. TS + R² + , if R = 3, S = 7, T = 2.
3. \(\frac{m}{2k}\) – n if k = 2, m = 8, n = -3.

Solution

To evaluate an algebraic expression we replace the letters by the numbers that we are told they equal. Then we find the value of the expression.

1. 5v + y
   5(3) + 2
   15 + 2
   17
2. TS + R²
   2(7) + 3²
   14 + 9
   23
3. \(\frac{m}{2k}\) – n
   \(\frac8{2(2)}\) – (-3)
   \(\frac84\) – (-3)
   2 – (-3)

To subtract a negative number, change the subtraction sign to addition, and change the negative sign to a positive sign.

2 + 3
5

Practice Problems

These problems will give you more experience with the material in this lesson.

1. Evaluate each of the following expressions using these values: d = 2, e = 3, f = 1
   a) 4e + ef
   b.) f – d – e
   c.)\(\frac{3e+f}d\)
2. Evaluate each of the following expressions using these values: b = 3, s = -1, w = 4
   a.) w² + 5s
   b.) bs – w
3. Evaluate each of the following expressions using these values: f = 2, g = 4, h = 1
   a.) 2g − 3h − f
   b.) f + h
   c.) g + h + f²
4. Using the formula E = RT (Earnings = hourly rate × number of hours worked), find the
   amount earned by each of the following people:
   a.) Jeff, who worked 35 hours at $9 an hour.
   b.) Diane, who worked 20 hours at $11 an hour.
   c.) Maria, who worked 18 hours at $12.50 an hour.

Answers to Practice Problems

1. a.) 15
   b.) -4
   c.) 5
2. a.) 11
   b.) -7
3. a.) 3
   b.) 3
   c.) 9
4. a.) 315 dollars
   b.) 220 dollars
   c.) 225 dollars