Definition: To evaluate an expression means to replace each variable with a given number and then calculate the value using the order of operations.
What does evaluate mean?
Evaluating means finding the numerical value of an expression once you know what the variables equal. You substitute, then compute.
What are the steps?
- Rewrite the expression with parentheses where each variable was.
- Put the given numbers inside those parentheses.
- Follow the order of operations.
How does it look with numbers?
Evaluate 3a2 – 2b + 10 when a = 4 and b = 7.
Substituting gives 3(4)2 – 2(7) + 10. Compute the exponent first: 42 = 16. Then multiply: 3 x 16 = 48 and 2 x 7 = 14. Finally 48 – 14 + 10 = 44.
Why use parentheses?
Parentheses protect negative values. Evaluate 5 – x when x = -3 by writing 5 – (-3) = 8. Without them, you might write 5 – -3 and lose track of the signs.
What is the common slip?
Squaring only part of a product. In 3a2, only a is squared, so you do not compute 3 x 4 = 12 and then square.
Example: For 6k – 9 with k = 2.5, the value is 15 – 9 = 6.