Arithmetic operators are the symbols used to indicate the type of arithmetic operation to be performed.
Types of arithmetic operators
The different ways of expressing arithmetic operators are as follows:
Addition: 3+1
Subtraction: 4-2
Multiplication: 3x4, 5*6, (4)(5), 6-7
Division: 8÷4, 5:3, 6/3
Hierarchy of arithmetic operators
Often in a mathematical expression there are several arithmetic operators, e.g.: 10 - 6 * 9 / 9
When this situation occurs, the operators must be solved in this order:
- First division and multiplication.
- Then addition and subtraction.
When there are two or more operators with the same hierarchy, one next to the other, solve the one that appears first from left to right. For example:
Problem |
Description |
10 - 6 * 9 / 9 |
solve the multiplication |
10 - 54 / 9 |
division is solved |
10 - 6 |
subtraction is solved |
4 |
|
Grouping operators
The first time a grouping sign was used was in 1399, in this case the dot .
, but it was not until 1470 that the parenthesis was used for the first time to group elements. There were other attempts, such as Giuseppe Peano and the use of the dots "". ... ... ..." or John Wallis and his ""vinculum"". Nowadays, parentheses, brackets and braces are used.
Hierarchy of operators
In addition to the arithmetic operators, we also find other operators such as the root and the power. When a mathematical expression contains several operators, they are resolved in the following order:
- Parentheses
- Square brackets
- Braces
- Power and root
- Division and multiplication
- Addition and subtraction
Example:
Problem |
Description |
{2-(4-3)}/5 |
subtraction is solved |
{2-1}/5 |
multiplication is solved |
2/5 |
division is solved |
In theory, you should write the brackets in the innermost part, then the square brackets and finally the braces; but not all follow this convention, so it is recommended that you first do what is more in the center of the operation until you reach the ends.
Combined or altered symbols
These are useful for precision approximations in calculus (left or right approximation), mechanical tolerances, or to show two equations in one, for example:

- ±
- ∓
Contribution created by: Néstor Arellano and Avilio Muñoz Vilchez.
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