Learn order of operations
Order of operations is the agreed sequence for evaluating expressions: grouping, exponents, multiplication or division, then addition or subtraction.
You will evaluate an expression in the correct order without skipping or reordering steps.
The idea in plain English
A calculation with several operations needs one agreed order so everyone gets the same result.
Multiplication and division share a level; addition and subtraction share a level. Work left to right within each level.
How to recognise this kind of question
- The expression contains two or more kinds of operations.
- You may see parentheses or exponents.
- There is usually no variable to solve.
Quick decision: Parentheses, exponents, multiply or divide left to right, then add or subtract left to right.
The method
- Evaluate expressions inside grouping symbols.
- Calculate exponents.
- Work multiplication and division from left to right, then addition and subtraction from left to right.
Worked examples
3 + 4 × 2
- Multiply first: 4 × 2 = 8.
- Then add: 3 + 8 = 11.
Answer: 11
18 ÷ 3 × 2 + 1
- Divide and multiply left to right: 18 ÷ 3 = 6, then 6 × 2 = 12.
- Add 1.
Answer: 13
Your turn—with help
4 + 3(5 − 2)
Need a hint?
Do the parentheses before multiplication.
4 + 3(3)
Show the answer and steps
- Parentheses: 5 − 2 = 3.
- Multiply: 3 × 3 = 9.
- Add: 4 + 9 = 13.
Answer: 13
Watch out for this mistake
Incorrect: 6 + 2 × 5 = 40
Why it fails: Adding first changes the expression's agreed meaning.
Do this instead: Multiply 2 × 5 first, then add 6 to get 16.
Quick check
Try these without looking. Then open each answer to check your thinking.
6 + 2 × 5
Need a hint?
Multiply before adding.
Show the answer and steps
- 2 × 5 = 10.
- 6 + 10 = 16.
Answer: 16
(8 − 3)²
Need a hint?
Parentheses first, then exponent.
Show the answer and steps
- 8 − 3 = 5.
- 5² = 25.
Answer: 25
20 ÷ 4 × 2
Need a hint?
Division and multiplication go left to right.
Show the answer and steps
- 20 ÷ 4 = 5.
- 5 × 2 = 10.
Answer: 10
Common mistakes
- Working strictly from left to right before multiplication.
- Treating addition as higher priority than multiplication.
- Applying an exponent to more than its stated base.
Practice tips
- Rewrite the expression after completing each priority level.
- Use one line per step so the order stays visible.