Order of Operations Calculator with Steps

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order of operations multiplication before division PEMDAS BODMAS

Order of operations: multiplication and division left to right (PEMDAS, BODMAS)

The question of which comes first, multiplication or division, has a short answer: neither, they go in the order they appear. Run the expressions below in the tool to see each operation in its own step and check where the wrong result comes from.

Priority levels and the classic mistakes

There are four levels: groups ( ) [ ] and braces; powers and roots; multiplication and division; addition and subtraction. Within one level, operations are done in the order they appear, left to right. In 8 ÷ 2 × 4 you do 8 ÷ 2 = 4 and then 4 × 4 = 16. Whoever does 2 × 4 = 8 first reaches 8 ÷ 8 = 1, the most common mistake. The same holds in 10 − 3 + 2: first 10 − 3 = 7 and then 7 + 2 = 9, not 10 − 5 = 5.
The English mnemonics hide this rule. In PEMDAS (used in the United States) and BODMAS (United Kingdom and India) the M comes before the D, and the A before the S, which suggests a priority that does not exist. The correct reading takes M and D as one pair and A and S as another. The order is explicit in BIDMAS, and all of the acronyms give the same result when applied left to right. In Brazil the equivalent is the list of levels above, without an acronym.
The viral expressions, such as 6 ÷ 2(1 + 2) and 48 ÷ 2(9 + 3), split opinions because of multiplication without a sign. The tool treats 2(1 + 2) as ordinary multiplication, at the same level as division: 6 ÷ 2 × 3 = 3 × 3 = 9, and 48 ÷ 2 × 12 = 24 × 12 = 288. Anyone who reads 2(1 + 2) as an indivisible block reaches 1 and 2. Textbooks and calculators differ here, so to be unambiguous in an exam or in code, write the parentheses that express your intent: 6 ÷ (2 × (1 + 2)) = 1.

Checked examples

Division then multiplication

Input: 8 ÷ 2 × 4
Expected output: 16

8 ÷ 2 = 4; 4 × 4 = 16.

Another chain

Input: 20 ÷ 4 × 5
Expected output: 25

20 ÷ 4 = 5; 5 × 5 = 25.

Subtraction then addition

Input: 10 − 3 + 2
Expected output: 9

10 − 3 = 7; 7 + 2 = 9.

Multiplication before addition

Input: 2 + 3 × 4
Expected output: 14

3 × 4 = 12; 2 + 12.

The viral expression

Input: 6 ÷ 2(1 + 2)
Expected output: 9

(1 + 2) = 3; 6 ÷ 2 × 3.

A variant

Input: 48 ÷ 2(9 + 3)
Expected output: 288

48 ÷ 2 = 24; 24 × 12.

With parentheses forcing the block

Input: 6 ÷ (2 × (1 + 2))
Expected output: 1

2 × 3 = 6; 6 ÷ 6.

Full tool FAQ

What is the order for solving a numeric expression?

Groups first (parentheses, then brackets, then braces, always innermost outward). Inside each group: powers and roots; multiplications and divisions, left to right; additions and subtractions, left to right. Example: 2 + 3 × 4² = 2 + 3 × 16 = 2 + 48 = 50.

Why are there parentheses, brackets and braces?

Does multiplication always come before division?

What is the difference between −3² and (−3)²?

How does it handle fractions and mixed numbers?

How do the sign rules work?

What about 6 ÷ 2(1 + 2), the viral expression?

What happens with roots that are not exact?

Which symbols does the tool accept?

When does the tool show an error?

Frequently asked questions

Does multiplication always come before division?

Under the school convention, no. They have the same priority and are done in the order they appear. In 12 ÷ 3 × 2 the result is 8 (4 × 2); if multiplication went first it would be 12 ÷ 6 = 2.

Do PEMDAS, BODMAS and BIDMAS give different results?

No. Only the names change (parentheses or brackets, exponents or orders or indices). The levels are the same, and multiplication and division, addition and subtraction are same-priority pairs in all three.

Why does the tool read 2(1 + 2) as 2 × (1 + 2)?

Because it is the reading that no primary-school case contradicts: the times sign is implicit and the parentheses are solved first. In step 2 you see the inserted times sign, and if you want another reading just add parentheses.

How does a phone calculator behave?

It varies. Basic calculators resolve each operation as you type, left to right, ignoring the priority of multiplication (2 + 3 × 4 gives 20 on them). Scientific calculators apply the correct order and give 14, like this tool.

Next steps

Priority levels and the classic mistakes

There are four levels: groups ( ) [ ] and braces; powers and roots; multiplication and division; addition and subtraction. Within one level, operations are done in the order they appear, left to right. In 8 ÷ 2 × 4 you do 8 ÷ 2 = 4 and then 4 × 4 = 16. Whoever does 2 × 4 = 8 first reaches 8 ÷ 8 = 1, the most common mistake. The same holds in 10 − 3 + 2: first 10 − 3 = 7 and then 7 + 2 = 9, not 10 − 5 = 5.

The English mnemonics hide this rule. In PEMDAS (used in the United States) and BODMAS (United Kingdom and India) the M comes before the D, and the A before the S, which suggests a priority that does not exist. The correct reading takes M and D as one pair and A and S as another. The order is explicit in BIDMAS, and all of the acronyms give the same result when applied left to right. In Brazil the equivalent is the list of levels above, without an acronym.

The viral expressions, such as 6 ÷ 2(1 + 2) and 48 ÷ 2(9 + 3), split opinions because of multiplication without a sign. The tool treats 2(1 + 2) as ordinary multiplication, at the same level as division: 6 ÷ 2 × 3 = 3 × 3 = 9, and 48 ÷ 2 × 12 = 24 × 12 = 288. Anyone who reads 2(1 + 2) as an indivisible block reaches 1 and 2. Textbooks and calculators differ here, so to be unambiguous in an exam or in code, write the parentheses that express your intent: 6 ÷ (2 × (1 + 2)) = 1.

Checked examples

Division then multiplication

Input: 8 ÷ 2 × 4
Expected output: 16

8 ÷ 2 = 4; 4 × 4 = 16.

Another chain

Input: 20 ÷ 4 × 5
Expected output: 25

20 ÷ 4 = 5; 5 × 5 = 25.

Subtraction then addition

Input: 10 − 3 + 2
Expected output: 9

10 − 3 = 7; 7 + 2 = 9.

Multiplication before addition

Input: 2 + 3 × 4
Expected output: 14

3 × 4 = 12; 2 + 12.

The viral expression

Input: 6 ÷ 2(1 + 2)
Expected output: 9

(1 + 2) = 3; 6 ÷ 2 × 3.

A variant

Input: 48 ÷ 2(9 + 3)
Expected output: 288

48 ÷ 2 = 24; 24 × 12.

With parentheses forcing the block

Input: 6 ÷ (2 × (1 + 2))
Expected output: 1

2 × 3 = 6; 6 ÷ 6.

Full tool FAQ

What is the order for solving a numeric expression?

Why are there parentheses, brackets and braces?

Does multiplication always come before division?

What is the difference between −3² and (−3)²?

How does it handle fractions and mixed numbers?

How do the sign rules work?

What about 6 ÷ 2(1 + 2), the viral expression?

What happens with roots that are not exact?

Which symbols does the tool accept?

When does the tool show an error?

Frequently asked questions

Does multiplication always come before division?

Under the school convention, no. They have the same priority and are done in the order they appear. In 12 ÷ 3 × 2 the result is 8 (4 × 2); if multiplication went first it would be 12 ÷ 6 = 2.