The order of operations is a standard for how math expressions should be evaluated. This standard guarantees that two different mathematicians will compute the same result from an expression. The order of operations is listed below.
- Parentheses
- Exponents and Logarithms
- Multiplication and Division
- Addition and Subtraction
Shown below is a basic example where the order of operations is used to produce the same result.
This example contains two operations: addition and multiplication. Since multiplication appears before addition, the multiplication operation should be evaluated first.
Then, the addition operation is performed as well, leaving the result of the calculation.
Note, if the addition operation had been performed before multiplication, a different result would be caluclated instead.
Parentheses are used to disambiguate and even change the meaning of a math expression. For example, the expression below uses parentheses to change the order of operations and produce a different result.
To compute the result of this expression observe that the first thing to do is evaluate expressions contained within parentheses. In this case, that means evaluate the expression . This is shown below.
Finally, we are left with only the multiplication operation which we perform.
This gives us the result .