Evaluate variable expressions with whole numbers
In algebra, letters (like x) stand in for numbers. 'Evaluating an expression' means you get to be the code-breaker! You are given the secret value of the letter, and your job is to plug it in and solve the problem.
Do this: Read the concept below, then try the quiz or activity.
Concept
A variable expression is a math phrase that contains numbers, operations (+, -, x, ÷), and at least one variable (a letter, like x or y). To evaluate it, you replace the variable with its given value and then perform the operations.
The Three-Step Process:
1. Substitute: Replace the variable with the number it stands for. It's a good idea to use parentheses when you substitute to keep things clear. 2. Simplify: Perform the calculations using the order of operations (PEMDAS). 3. Solve: Find the final value of the expression.
Example 1: Evaluate 5x - 3 when x = 4.
1. Substitute: Replace 'x' with 4.
* 5(4) - 3
2. Simplify: Remember that 5x means 5 *times* x.
* 5 x 4 = 20
* Now the expression is 20 - 3.
3. Solve:
* 20 - 3 = 17.Example 2: Evaluate y/3 + 2 when y = 12.
1. Substitute: Replace 'y' with 12.
* 12/3 + 2
2. Simplify: Division comes before addition (PEMDAS).
* 12 ÷ 3 = 4
* Now the expression is 4 + 2.
3. Solve:
* 4 + 2 = 6.Example with Multiple Variables: Evaluate 2a + 3b when a = 5 and b = 6.
1. Substitute: Replace 'a' with 5 and 'b' with 6.
* 2(5) + 3(6)
2. Simplify: Do both multiplications.
* 2 x 5 = 10
* 3 x 6 = 18
* Now the expression is 10 + 18.
3. Solve:
* 10 + 18 = 28.Key Idea: The variable is just a placeholder. Once you know its value, the problem becomes a regular numerical expression.
Try it
Practice: Evaluate variable expressions with whole numbers.