What is the right order of the mathematical operations?

First of all I want to clarify that the order of mathematical operations, this is, the order according to which an operation must be solved such as the following one: `2+3xx5` is a convention. What does it mean? It means that a long time ago, mathematicians have decided about what should be the order through which the operations should be solved. It has nothing to do with logic. It is only a convention similar to what had been agreed concerning the fact that if between a number and brackets there isn’t any arithmetic sign is because it is a multiplication. Some people decided to follow that order which has been spread out and followed by everybody. From that moment on it has become a mathematical rule, and it is an obligation to respect that order and the communication among mathematicians became easier and easier. In other words, it consists of a mathematical notation aimed at simplifying the writing, showing people which are the operations that must be firstly solved.

For all that, here we have the right order to solve mathematical operations:

• 1º Parentheses;
• 2º Exponents;
• 3º Multiplication/Division; (from the left to the right)
• 4º Addition/Subtraction. (from the left to the right)

Let’s see some examples:

• `2+3xx5=2+15=17`
• `(2+3)xx3^2=5xx3^2=5xx9=45`

It is also important to say that all the operations involving logarithms, trigonometric ratios or another kind of function, those ones must be firstly solved. It is not possible to solve `3+f(2)` before knowing the value of `f(2)`.

Let’s see two more examples so as to help you to better understand:

• `6 + log(100) * e^0=6+2xxe^0=6+2xx1=6+2=8`
• `3 Cos(pi) (2^2 + 1)^2 = 3 xx (-1) xx (4+1)^2=3 xx (-1) xx 5^2 = 3 xx (-1) xx 25 = -75`

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