Combined Operations


It is an expression made up of numbers in various operations and grouped in different ways by parentheses, brackets, and keys. Combined operations are those in which several arithmetic operations appear to be resolved. To obtain a correct result, it is necessary to follow some rules and take into account the priority between the operations. Combined operations cannot be done randomly, they must follow an order.

To carry out combined operations (that is, when there are additions, subtractions, multiplications and divisions in the same expression) the following steps are followed:

  • First, the operations inside the parentheses are performed.
  • Then the powers are resolved.
  • Then the multiplications and divisions, from left to right.
  • Finally, addition and subtraction, from left to right.

To solve combined operations we must master everything previously studied.

  • The mission of parentheses is to unite or what they affect.
  • The multiplication signs come together more than the addition and subtraction signs, that is, when two numbers are joined by the multiplication sign they form an inseparable block, while if they are joined by an addition or subtraction sign they are looser.
  • You must have prior knowledge of the properties of the operations so that the process is not incorrect.
  • To be able to add or subtract two numbers must be loose, we cannot add two numbers if one of them is joined on the other side to another expression by means of a multiplication sign.
  • Combined operations must be resolved in several steps, everything that is not resolved in one step must be copied back as it was, keeping its exact position.
  • Therefore, before beginning to solve the combined operations, the expression must be observed and a procedure to be followed proposed, which is done before and after.
  • As a general rule, it is advisable to solve the exercises starting from the inside of the parentheses to the outside, then continue with the multiplications and finish doing the remaining additions.

In combined operations without grouping signs, the first step is to apply multiplication or division, as appropriate; then addition or subtraction, according to the order in which they appear from left to right.

In combined operations with grouping signs, first determine what is resolved between the signs, keeping in mind that what is inside the parentheses is resolved first, then the brackets, and then the keys, if any. Remembering that the rules of combined operations must always be taken into account without grouping signs.