Combined operations

When we do many operations, in order to save time, positive numbers can be written without the sign if they are being subtracted.

For example, if we have the sum: $$(+3)+(-6)$$ we can write: $$3+(-6)$$

To do combined operations (that is, when in the same expression addition, subtraction, multiplication and division are present) we must follow these steps:

  1. First do the operations in brackets.
  2. Then we operate the powers.
  3. Then the multiplications and divisions, from left to right.
  4. Finally, the addition and subtraction, from left to right.

For example, to perform the following calculation: $$(5\cdot7+6)-\dfrac{8}{2}=$$ we will follow these steps:

  1. We do the operation in brackets: $$(5\cdot7+6)$$ However, as there are two operations, we must think first about the order in which the operations should be done. Looking at points 3) and 4) of the previous method. It is clear that the multiplication is performed first and then addition. That is: $$5\cdot7=35$$ $$35+6=41$$ Thus, we have: $$(5\cdot7+6)=41$$. We can now move to the next step.
  2. There is no power, so we can pass to the next step.
  3. Now it comes the division: $$\dfrac{8}{2}=4$$. Since there is no more division or multiplication, we continue with the last point.
  4. We have come to the operation: $$41-4=$$. It is an ordinary subtraction, and we get: $$41-4=37$$. So, the result is: $$(5\cdot7+6)-\dfrac{8}{2}=37$$