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What is the Order of Operations?

Order of Operations Practice Problems Quiz

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Video Transcript:

This video is about answering the question what is the order of operations. You can get this pemdas worksheets for free by clicking on the link in the description below.

Before we do some order of operations practice problems, I want to first go over what exactly the order of operations are. Typically, when we talk about order of operations, we refer to it as PEMDAS. These are the order that you need to perform the operations in a problem. Each one of these stands for something different. The P stands for parentheses, which would be the parentheses symbols if there are any. The e stands for exponents. You would do those next and those are the little numbers up here like this two, right here would be an exponent. The M stands for multiplication, the d stands for division, A stands for addition and finally the S stands for subtraction. Now the only other thing I need to make mention of is that a lot of times people get confused around the M the d the a and the S. This is because it seems like you should always do multiplication first or always do division first. In reality these two go together and these two go together. You always perform these two from left to right as well as addition and subtraction from left to right. That means that sometimes you’ll do division before you do multiplication and you’ll do subtraction before you do addition. It just depends on which one is on the left and which one is on the right in your problem.

Let’s do the first order of operations problems on our pemdas worksheet. Now the first problem we’re going to go over is number two, which is three plus five times four. In order to determine which operation, you should perform first you have to remember the order of operations, or PEMDAS, as a cheat. For this problem we don’t have any parentheses so we’re going to go past that step. Then we check for exponents, we also don’t have any exponents so we skip that step. The next step is multiplication and division. If you look, we do have a multiplication part of this problem. The first thing we’re going to do is we’re going to perform that multiplication part. We’re going to do 5 times 4. We bring down this 3 and we do 3 plus and then 5 times 4 is 20. That turns into that then the next step is to just perform the last operation. 3 plus 20 is 23. Our final answer has to be 23.

Moving on to number 3 showing you guys what is the order of operations, we have negative 2 plus four in parenthesis times 10. For this pemdas problems we’re still going to follow the order of operations. The first thing we have to check for is parentheses, that’s what P is. If we look we do have a set of parentheses here. The first thing we have to do is we have to perform the operations inside of the parentheses. In this case we have to add negative 2 plus 4. We’re going to add those two together first because they’re in the parentheses. When we add negative 2 plus 4 you will get positive 2, then you bring down the x and the 10. Now we have positive 2 times 10. Our parentheses are done, now we don’t have any exponents so we can cross that off and we’re all into multiplication. Right here we do 2 times 10 and 2 times 10 is 20 and that’s going to be our answer.

Moving on to our next order of operations example number 6 gives us 4 minus 10 divided by 5 times 7. The first thing we have to do is we have to determine which is the first part of the pemdas practice problems that we need to complete according to our order of operations. We’re going to just go down the list. P stands for parentheses, there are no parentheses so we can ignore that and we’re going to skip it. E stands for exponents, there are no exponents in this one so we’re going to skip it. M stands for multiplication and we have a multiplication part right here. Five times seven and D stands for division and we have a division component right here. M and D go from left to right. They are actually the same step and you perform them from left to right. A very common mistake is to always complete multiplication before division. Now in this problem the division is on the left of the multiplication symbol which is on the right. That means that you’re going to perform this part first and then you’re going to do this multiplication part second. We’re going to do ten divided by five 10 divided by 5 is 2 then we’re going to simplify that and just make it 2. Next we have to bring down the other parts of the problem. This 4 comes down this minus comes down and this multiplication and 7 come down. For the second step we have 4 minus 2 times 7 now and for this one, 2 times 7 comes first because this is multiplication. We know that multiplication comes before subtraction. This multiplication is going to get done before this subtraction so we’re going to do 2 times 7 first before we do the subtraction part. 2 times 7 is 14 and then we bring down this 4 again and this minus sign again. Now we’re left with 4 minus 14 and 4 minus 14 is negative 10. Our solution is going to be negative 10.

The last order of operations example that we’re going to do on our order of operations worksheet is number 8. This problem gives us 2 to the 4th plus 5 times 6 divided by 3. In parentheses in order to complete these in the correct order we just follow our order of operations. The first thing we’re going to do is anything in parentheses. If you look, we have a set of parentheses here which has 6 divided by 3 inside. The very first thing we need to do is this part, six divided by three is two and then you bring the rest of the problem down. Two to the fourth comes down here this plus five comes down and then this multiplication symbol also comes down. The next thing we have to check for is exponents. In this case we have a term that has an exponent, that’s going to be our second step for this problem. Two to the fourth power is two times two times two times two, this would be 2 times 2 is 4 4 times 2 is 8 8 times 2 is 16. That’s going to be 16. Then we bring down the rest of our problem. Now the problem is 16 plus 5 times 2. The next thing we need to look for is multiplication and division. We have 5 times 2, this multiplication symbol goes before this addition symbol so we’re going to multiply those two together. 16 comes down plus 5 times 2 and 5 times 2 is 10. Finally, we do 16 plus 10, that’s our last step, and that’s going to give us 26 as our final answer. You can try all the practice problems by downloading the free order of operations worksheets with answers above.