Free Teacher Resources

Order of Operations

Enter an expression and watch PEMDAS unfold one operation at a time, with the reason for each step.

Try:

Use + − * / and parentheses ( ). Multiplication must be written with *.

  1. 1

    3 + 4 * (5 - 2)

    Subtract: 5 - 2 = 3

  2. 2

    3 + 4 * (3)

    Remove the parentheses around 3.

  3. 3

    3 + 4 * 3

    Multiply: 4 * 3 = 12

  4. 4

    3 + 12

    Add: 3 + 12 = 15

Answer

15

About the Order of Operations Solver

Ask a class to solve 3 + 4 × 5 and you'll get at least two answers, which is exactly the problem order of operations exists to fix. This tool takes any expression with addition, subtraction, multiplication, division, and parentheses, then solves it the way a student should: working from the innermost parentheses outward, multiplication and division left to right, then addition and subtraction left to right.

Each step shows the expression as it stood right before that operation happened, with an optional explanation of why that particular piece was chosen next rather than something else in the expression.

How to use it in your classroom

  1. Type an expression using +, -, *, /, and parentheses in the input box.
  2. Try one of the four example expressions if you want a ready-made problem instead of typing your own.
  3. Step through the solution, where each line shows the expression before that step and which operation just happened.
  4. Click "Show reasoning" on a step to see why that operation was performed at that point rather than another part of the expression.

Tips from the classroom

  • Use the nested-parentheses example, 2 × (6 − (1 + 1)), to show that the innermost parentheses always resolve first, even when there's more than one layer.
  • Build an expression with both multiplication and addition outside any parentheses so students see multiplication happen first even though addition appears earlier when reading left to right.
  • Open the reasoning on a step only after a student has guessed what should happen next — it works better as a check than as the first thing they read.
  • Try an expression that divides by an expression equal to zero on purpose, so students see how the tool reports that as an error rather than a silent wrong answer.

Frequently asked questions

What operators and symbols can I use in an expression?

Addition (+), subtraction (-), multiplication (*), division (/), and parentheses. Implicit multiplication (writing two numbers next to each other with no symbol) isn't supported — use * explicitly.

What happens if I type an incomplete or invalid expression?

The tool shows an error message explaining the problem, such as an unexpected character or a division by zero, instead of attempting to guess what you meant.

Does it follow the standard left-to-right rule for operations at the same level?

Yes, when multiple operations of the same precedence appear outside of parentheses, it resolves them in left-to-right reading order, matching how the rule is taught.