Video:What Is the Order of Operations?

Transcript:What Is the Order of Operations?

Hi, I'm Jen D'Amore for About.com, and this video is all about the order of operations. The order of operations is a rule that lets you know what to do first, when solving mathematical equations.

Order of Operations: Parentheses Are First

Let's say you're looking at a complex equation filled with multiplication, addition, subtraction, division, and a number of parentheses.  The order of operations makes it clear what to do first. First rule:  always complete the smaller equations that are inside parenthesis before moving outside of them. Think of it as always working from the inside out. 

Rest of the Order of Operations

That also means computing exponents and roots next.  Obviously, if there is an integer with an exponent or root inside the parenthesis, it will need to be calculated in order to solve what is inside the parenthesis, so it would be done first. The next priority is multiplication and division, followed by addition and subtraction.

Examples Using Order of Operations

Let's look at a few examples. If you're solving a problem that doesn't contain any brackets, like this one, be sure to remember to do any multiplication or division, before doing any addition or subtraction.  Reversing the order will calculate an incorrect answer.

For example:

1+4x6 =  25

1+4x6 = 30

In the first answer, 4 is multiplied 6 first, equaling 24.  Then 1 is added resulting in 25.

In the second answer, which is incorrect, 1 is added to 4, equaling 5.  then 6 is multiplied by 5, resulting in the incorrect answer of 30. 

Luckily, as algebraic equations get more complicated, brackets are involved. So, whenever possible, use them.  

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