Can Your Homeschooler Solve This Math Problem? (PEMDAS Review)

[00:00:00]So, let's see if your homeschooler is really understanding math. So, if your child has taken at least homeschool pre-alggebra, this should be a very easy problem for them to solve without a calculator. Okay, so here is the problem. We have -3^ 2ar + 6 * 4 + 1 in parenthesis. Now, before I get into the solution, if you need help homeschooling math, make sure to check out my award-winning homeschool math program.

[00:00:30]I'll leave a link to it in the description below. Okay, so let's go and get into this problem. Now, the first thing we need to be thinking about is the order of operations. Now, uh in mathematics, uh things like addition, subtraction, multiplication, division, and powers, these are mathematical operations. Okay, these are mathematical operators and we need to know what is the correct order to do a prom because uh depending on how what order you take, you're going to generate different values. Now, of course, there's only one correct order. So, the correct order to take is defined by uh the order of operations which is kind of indicated by this nice acronym. And this little phrase right here is called PEMDOS, right? PEMDOS. And these letters of course stand for something. This is a checklist. we're going to follow and we're going to follow it from left to right. Now, I'm going to explain uh this PEMDOS here uh real quick here in a second, but I want to give you a nice lovely memory aid that goes along with this, and that is please excuse my dear aunt Sally. Once again, please excuse my dear aunt Sally. People have been saying this for decades. Probably my greatgrandparents way back in the 1920s and 30s were saying this. I don't know what Aunt Sally did, but we thank Aunt Sally for her awesome little phrase. But anyways, that's how you can remember PEMDOS. Now, let's go ahead and get into uh the order of operations. So, the P here stands for parenthesis. So, we're going to do parenthesis first.

[00:02:03]Obviously, we have some parentheses in our problem. But this P is also uh these type of things like brackets and these type of brackets like this. Really, it's technically uh grouping symbols. Okay?

[00:02:15]So, anytime you see grouping symbols, we're going to go to those first. Now, sometimes you have a problem where you have parentheses inside parentheses or parentheses inside brackets. So, way this works, you're going to go to the innermost parenthesis, finish that, and just kind of work your way out from there. Okay, so that's what the P stands for. And now, let's move on to E. So, E is effectively like powers. Okay, you can think of that as powers. And somebody might be saying, "Well, if it's powers, why don't they put another P here?" Well, it would be kind of confusing. Real quick, when you have a power, there's actually two components that make up the power. This little number in the top right is called the exponent. And this big number down here is called the base. Okay? The entire thing is a power. So, this is 2 to the third power. Again, this little number up here is the exponent. So, e really stands for exponents, but that's what it means. It means, hey, do powers. Okay.

[00:03:13]Now the next part of or the remaining part of the order of operations gets a lot of confusion. Okay? And for good reason. I don't think uh this is stressed often enough uh or well enough in a lot of textbooks. But let's just quickly define what MD, AA and S stand for. So M is multiplication, D is division, A is addition, S is subtraction. Now I am saying that this is a checklist that goes from left to right. So most people would say, "Oh, well, you have to do all of multiplication and then you move on to division uh like so." But that's not the way it works. Okay? So really the way it works this you want to think of these as two groups. So the next thing you're going to do you're going to do is multiplication or division. Okay? You're going to do multiplication or division.

[00:04:00]Whatever you see first from left to right. So if I see multiplication then division like this, I'm going to do it from left to right this way. But if I see division before multiplication from left to right, I will do it this way.

[00:04:13]Okay. Same thing for addition and subtraction. Subtraction excuse me, it's what I receive first from left to right.

[00:04:21]Okay. Okay, so now that you have a strong understanding of the order of operations, it's pretty clear that we have to start right here with these parenthesis. And then we'll just kind of just take one step at a time as we get through uh you know um get going and uh into the solution of this problem. Now, a lot of you might be saying, well, you know, I want to give this problem another try. That's fantastic. If you there was something that was, you know, confusing you, you should try this problem and not wait for me to show you what to do. Okay, so let's go ahead and get into it right now. So the first thing I'm thinking about PEMDOS, so it's parentheses. So I have to go where the parentheses are at and go inside of the parenthesis and clean up everything there. So uh 4 + 1, that's pretty easy.

[00:05:04]That is five. Okay, so no problems right here. And the next thing I'm going to show you is where there is a lot of confusion. So in terms of the order of operations, okay, uh let's just put this PEMDOS back up, right? PM D, we just uh took care of our parentheses.

[00:05:25]There's no more parentheses. Now, some always say, hey, there's parentheses here. Well, there's nothing to do inside of it, right? We don't have any math, problem, uh any operations to do. So, this simply just means uh 6 * 5 at this point. Okay. So, next thing on our list is uh exponents, powers. So, do we have any powers? Yes, indeed. Right here. So, we're going to have to take care of that before we move on to any multiplication or division and addition and subtraction. Now, this -3 squared we have to figure out because this is the powers, right? We have to handle this exponent part first. But here is the thing. A lot of people think that this -3^2 is the same thing as taking -3 to the second power. Okay, these two things are uh different. Okay, this does not mean do this. Okay, this is something different. [snorts] And a lot of people think, oh, I'm going to take -3 and multiply by itself and I'm going to get a positive 9. Well, that's incorrect.

[00:06:29]Let's go and take a look why. Okay. And if you can understand this, this is going to save you a lot of heartache in the future. Okay. So, -3 squared, this is not our situation, but let's just kind of take a look at what this means.

[00:06:41]-3 enclosed in parentheses squared means take -3 and multiply by itself two times, right? So, negative * a negative is a positive. So, our answer is going to be positive 9. Now this right here what we're actually have to do in this problem is -3^2 this does not mean this and it can be easily confused. So if you've been confused or if you are confused you know uh I understand right but let's try to uh clear up that confusion right now. What this means -3 squared where there's no parenthesis at that is that this squared right here this exponents it's acting upon this. So really I want you to interpret this situation as the opposite of 3^ squared.

[00:07:28]Okay? Or the negative of 3^ squar. So 3^2 is 3 * 3 that's 9. So this is -9.

[00:07:35]Okay? So uh you know you need to be able to distinguish where that negative sign is in a power. Okay. Another way you can kind of think of that is this is a negative of 3^ squared. And um let's get let's see if we can make this even a little bit more clear here in a second.

[00:07:51]Uh so -3^ squar technically this is like a -1. So that would be like a -1 * a 3^ squar. So when we're thinking about the order of operations we're going to do powers before multiplication. So that's a positive 9. So again this is going to be a - 9. All right. So however you want to understand it but you need to recognize the difference when you're faced with a situation like this.

[00:08:16]they're not going to uh interpret it as a uh you know taking a power of this entire negative -3. Very very common misunderstanding and hopefully we kind of cleared up that confusion. All right.

[00:08:29]So the answer here is -9. All right. So now at this point we're doing our PEMDOS. We're going to have to take care of power. So this -3^2 is -9 not positive 9. And so we have 9 + 6 * 5.

[00:08:45]All right. So 6 * 5 and uh that's going to be pretty easy to do here. So 6 * 5 of course is 30. So -9 + 30 is 30 - 9 and of course the correct answer would be 21. Now if you're struggling with anything here, okay, uh what you want to do is just make note. Okay, like okay, I don't understand this. I don't understand that. I don't understand this. Maybe it's powers. Maybe it's positive negative numbers. Uh maybe it's something else. Okay. Well, this becomes your kind of like your math shopping list, right? So, what you have to do is go to the math store and pick up these skills. You like, hey, I need one of these, one of those, and one of these.

[00:09:25]And that's how you improve in math. So, with that being said, I definitely wish you all the best in your mathematics adventures. Thank you for your time and have a great day.