Table shows order of common math operations, which should be applied while performing arithmetic calculations such as addition, subtraction, multilication, division etc.

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Order of operations#

Order (precedence)	Operation name	Operation symbol
1	curly brackets	Show source $\{\}$
2	square brackets	Show source $[]$
3	curly brackets	Show source $()$
3	exponentiation and root	Show source $\begin{aligned}x^n\\ \sqrt[n]{x}\end{aligned}$
4	multiplication and division	Show source $\begin{aligned}x \cdot y\\ x \div y\\ x/y\\ x:y \\ \frac{x}{y}\end{aligned}$
5	addition and subtraction	Show source $\begin{aligned}x+y \\ x-y \end{aligned}$

Some facts#

If arithmetic expression contains more than one operation (e.g. addition and multiplication), then in the general case we can get different results depending on applied operation order.
To solve this problem we should follow the common operation order rules was developed.
To get correct result, we should perform arithmetic operations in the following order:
- operations in brackets - curly brackets first (the highest precedence), square brackets and finally expressions in round brackets (the lowest precedence),
  
  ⓘ Example: In the expression $2 \cdot \boxed{\left(3 + 4\right)}$ we should perform addition in brackets first, and the multiplication next.
- exponentiation and root,
  
  ⓘ Example: In the expression $2 \cdot \boxed{3^4}$ we should perform exponentiation first (raise three to power four), and perform multiplication next.
- multiplication and division,
  
  ⓘ Example: In the expression $\boxed{2 \cdot 3} + 4$ we should perform multiplication first, and addition next.
- addition and subtraction.
  
  ⓘ Example: In the expression $2 - 3 + 4$ the order of operations doesn't matter, we can perform addition first, and subtraction next or vice versa. The addition and subtraction have the same precedence.
If you want to know more about properties of various math operations check out our other table: Number operations.

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math_operations_order · math_operations_precedence · order_of_operations

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TABLE · MATH · A -> Z (all)

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