Order of Operations: PEMDAS and BODMAS
6 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
When an expression has several operations, the order you do them in changes the answer. Mathematicians agreed on one standard order so everyone gets the same result. In the US it is remembered as PEMDAS and in the UK and India as BODMAS. They describe the same rules.
The rule
| Step | PEMDAS | BODMAS |
|---|---|---|
| 1 | Parentheses | Brackets |
| 2 | Exponents | Orders (powers and roots) |
| 3 | Multiplication and Division (left to right) | Division and Multiplication (left to right) |
| 4 | Addition and Subtraction (left to right) | Addition and Subtraction (left to right) |
Multiplication and division share the same level, as do addition and subtraction. Within a level, work from left to right. “PEMDAS” does not mean multiplication always comes before division.
Worked example
Evaluate 6 + 2 × (5 − 3)² ÷ 4.
- Brackets: 5 − 3 = 2, giving 6 + 2 × 2² ÷ 4.
- Exponent: 2² = 4, giving 6 + 2 × 4 ÷ 4.
- Multiplication and division left to right: 2 × 4 = 8, then 8 ÷ 4 = 2, giving 6 + 2.
- Addition: 6 + 2 = 8.
Common traps
- Negative bases: −3² = −9 because the exponent is done first and then the minus is applied. (−3)² = 9.
- Left to right: 24 ÷ 4 × 2 = 12, not 3. Divide first (6), then multiply (12).
- Implied multiplication: 8 ÷ 2(2+2) is ambiguous. Read strictly left to right it is 8 ÷ 2 × 4 = 16, but some textbooks treat 2(2+2) as a single unit and get 1. Good writing avoids this with extra brackets.
- Fractions: a fraction bar groups the top and bottom. (3 + 5) ÷ 2 needs brackets when typed on one line.
How calculators handle it
A scientific calculator, including ours, follows the order of operations, so 2+3*4 displays 14. Older basic calculators evaluate strictly in the order you press the keys and would give 20. When in doubt, add brackets. The scientific calculator shows a live preview so you can check that it read your expression the way you meant.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Calculate 7^4.
Show answer
7^4: 2,401
- Add 2/3 + 3/4.
Show answer
Simplified fraction: 17/12
Frequently asked questions
Is PEMDAS the same as BODMAS?
Yes. Parentheses = Brackets, Exponents = Orders. Multiplication and division are done left to right at the same level in both.
Do multiplication and division have equal priority?
Yes. Do them in the order they appear from left to right.
What is 6 ÷ 2 × (1 + 2)?
Brackets first: 6 ÷ 2 × 3. Then left to right: 3 × 3 = 9.
Why do some expressions go viral with different answers?
Usually because of implied multiplication, which has no single universal convention. Adding brackets removes the ambiguity.
Try it yourself
Exponent CalculatorRaise any number to a power, including negative and fractional exponents.
Fraction CalculatorAdd, subtract, multiply and divide fractions with simplified and mixed-number answers.Keep learning
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