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Video:What Are the Rules for Order of Operations?

with Bassem Saad

Want to learn about the rules for order of operations? Here, see helpful tips for using the order of operations correctly.See Transcript

Transcript:What Are the Rules for Order of Operations?

Hi, my name is Bassem Saad. I'm an associate math instructor and Ph.D. candidate. I'm here today for About.com to introduce the rules for the order of operations.

Basic Rules for Order of Operations

So say you had an expression: five, times six, plus two. And let's say you decided to multiply five, times six first, and then add the two. So five, times six is 30, plus two, that's 32. And that's definitely a number, but then say you decide to add the two and the six first. So you have five, times six, plus two. Well, six, plus two is eight, and five, times eight is 40. Notice the same expression we get two different answers depending on what we decide to do first. Well, the order of operations makes a clear distinction which one you should do first.

Additional Rules for oAder of Operations

So, here is the order of operations: The first thing you want to do is evaluate all terms inside the parentheses of an expression; then evaluate all exponents and roots; after you evaluate all exponents and roots, you want to evaluate all multiplication and division, from left to right; finally, you want to evaluate the addition and subtraction, from left to right. So let's take a look at this example. Recall that parentheses comes first in the order of operations, so we want to evaluate everything inside the parentheses first. Notice inside the parentheses we have an exponent and some sums. Exponent comes next in the order of operations, so we evaluate two squared before we subtract or add, to give us four. So we've got six, minus four, plus one. Now minus and plus are at the same order of operations, so we evaluate from left to right. That's six, minus four – that's two. Two, plus one – that's three. And we no longer need the parentheses, so we drop them. So that's three, divided by three, equals one. So now we know the order of operations.

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