Evaluating Simple Algebraic Expressions: Fifth Grade Mathematics

Evaluating an algebraic expression means substituting a given numerical value in place of the variable and calculating the resulting value using the order of operations.

The Substitution Method

To evaluate an algebraic expression:
1. Replace every occurrence of the variable with the assigned number. Use parentheses around the substituted number to preserve multiplication.

2. Evaluate the numerical expression using PEMDAS.

+--------------------------------------------------------------------------+
|                  SUBSTITUTION AND EVALUATION PROCEDURE                   |
|                                                                          |
|       Expression:  3x + 7,  when x = 4                                   |
|                                                                          |
|       Step 1: Substitute 4 in place of x:                                |
|               3(4) + 7                                                   |
|       Step 2: Multiply 3 * 4:                                            |
|               12 + 7                                                     |
|       Step 3: Add:                                                       |
|               19                                                         |
|                                                                          |
|       Value of expression is 19.                                         |
+--------------------------------------------------------------------------+

Expressions with Two Variables

When an expression contains two different variables (such as 2a + 3b), substitute the designated value for each variable independently.

Evaluating 4m - 2n, when m = 8 and n = 3:
  Step 1: Substitute: 4(8) - 2(3)
  Step 2: Multiply:   32 - 6
  Step 3: Subtract:   26

Fractions and Division in Expressions

When a variable appears in the numerator or denominator of a fraction bar, treat the fraction bar as a grouping symbol: Evaluate (x + 6) / 2 when x = 8: Substitute: (8 + 6) / 2 = 14 / 2 = 7.

Exercises and Solutions

Exercise 1: Single Variable Evaluation. Evaluate the expression 5n - 4 when n = 6, and when n = 9.

Solution 1: When n = 6: substitute 6 for n: 5(6) - 4 = 30 - 4 = 26. When n = 9: substitute 9 for n: 5(9) - 4 = 45 - 4 = 41.

Exercise 2: Two-Variable Multi-Step Expression. Evaluate the algebraic expression 3(x + y) - 2x when x = 5 and y = 4.

Solution 2: Substitute x = 5 and y = 4 into the expression: 3(5 + 4) - 2(5). Evaluate parentheses first: (5 + 4) = 9. Rewrite: 3(9) - 2(5). Perform multiplications: 3 * 9 = 27, and 2 * 5 = 10. Rewrite: 27 - 10. Perform subtraction: 27 - 10 = 17. The value of the expression is 17.