Order of Operations

  1. Parantheses
  2. Exponents and Logarithms
  3. Multiplication and Division
  4. Addition and Subtraction

The order of operations is an agreed upon standard that describes what operations should be performed first in a math expression. By ordering which operation should happen before another operation, two different mathemeticians should be able to look at a math expression and calculate the same result. For example, without ordering, the expression one plus two multiplied by three is ambigous:

Should we add one with two first, and then multipy by three? Or should we multiply two with three and then add one? The different approaches produce different results.

The solution is to agree as mathemeticians upon the order in which operations should be performed. For this example, the order of operations specifies that multiplication should be performed before addition.

As a rule of thumb, if you are unsure of what should happen first, parantheses should be added to make your intention clear.

Order

Parantheses

Expressions contained within parantheses should be evaluated first before any operation.

Exponents and Logarithms

Multiplication and Division

Addition and Subtraction