Evaluating Expressions
Substitute numbers for variables then follow order of operations.
About this topic
To evaluate an expression you substitute a number for each variable and then calculate following the order of operations. If x = 4, then 3x + 5 becomes 3(4) + 5 = 17. Putting brackets around substituted values helps avoid sign errors, especially with negatives.
Evaluating turns a general rule into a specific answer. It is how formulas for area, speed or interest are used in practice, and it is also how you check whether a proposed solution to an equation really works. With more than one variable, substitute them all: if a = 2 and b = −3, then a² − 3b = 4 + 9 = 13.
Consider the temperature formula F = 9C/5 + 32. For C = 20, substitute to get 9(20)/5 + 32 = 36 + 32 = 68 degrees Fahrenheit. In science class you might evaluate distance = speed × time for several times to build a table of values, which later becomes a graph.
Typical errors include forgetting brackets so that x² with x = −3 is written as −3² and computed as −9 instead of 9. Another is substituting into the wrong place or dropping the multiplication sign, turning 3x with x = 4 into 34. Write the substitution on its own line, then compute step by step, and check the result for reasonableness.
Key ideas
- Replace each variable with its value
- Use brackets for negative substitutions
- Compute carefully
Quick check
Use cases: where Evaluating Expressions helps
- Homework: review the key idea behind Evaluating Expressions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Evaluating Expressions without notes.
- Visual learning: play with the interactive lab to see how Evaluating Expressions changes when you adjust its inputs.
- Teaching a friend: explain Evaluating Expressions in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Evaluating Expressions?
Substitute numbers for variables then follow order of operations.
What will I learn in Evaluating Expressions?
Replace each variable with its value. Use brackets for negative substitutions. Compute carefully.
Is Evaluating Expressions part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Evaluating Expressions lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Evaluating Expressions?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.