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 nameOperation symbol
1curly bracketsShow source{}\{\}
2square bracketsShow source[][]
3curly bracketsShow source()()
3exponentiation and rootShow sourcexnxn\begin{aligned}x^n\\ \sqrt[n]{x}\end{aligned}
4multiplication and divisionShow sourcexyx÷yx/yx:yxy\begin{aligned}x \cdot y\\ x \div y\\ x/y\\ x:y \\ \frac{x}{y}\end{aligned}
5addition and subtractionShow sourcex+yxy\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(3+4)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 2342 \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 23+4\boxed{2 \cdot 3} + 4 we should perform multiplication first, and addition next.
    • addition and subtraction.
      ⓘ Example: In the expression 23+42 - 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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