Order of Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Order of Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The agreed-upon sequence for evaluating expressions: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Without rules, 2 + 3 \times 4 could mean 20 or 14. We agree to multiply first: 14.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Convention ensures everyone gets the same answer from the same expression.

Common stuck point: Forgetting that \times and \div have equal precedence (go left to right).

Sense of Study hint: Try breaking the problem into smaller steps -- compute each operation one at a time following PEMDAS order.

Worked Examples

Example 1

easy
Evaluate 3 + 4 \times 2.

Solution

  1. 1
    Identify the operations present: multiplication and addition.
  2. 2
    Apply PEMDAS: multiplication before addition. Compute 4 \times 2 = 8.
  3. 3
    Now add: 3 + 8 = 11.

Answer

11
The order of operations (PEMDAS/BODMAS) tells us to perform multiplication before addition, even when addition appears first in the expression.

Example 2

medium
Evaluate 2 \times (3 + 5)^2 - 10 \div 2.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Evaluate 18 - 3 \times (4 + 1) + 2^3.

Example 2

hard
Evaluate 5 + 3^2 \times 2 - (12 \div 4 + 1).
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Background Knowledge

These ideas may be useful before you work through the harder examples.

additionsubtractionmultiplicationdivision