Mathematical tables: operations precedence
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.
ⓘ 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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