18 ÷ (3 + 6 ÷ 2 × 1) — Many Will Get This WRONG!

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[00:00:00]18 divided by parentheses 3 + 6 / 2 * 1 and parentheses. Now, if you think you have the answer, go ahead and put that into the comment section. I'm going to walk through and show you exactly how to solve this problem step by step. Now, of course, this looks like a very simple problem, but I guarantee you a lot of you are going to be shocked that you're going to get the wrong answer. So, the key to getting the right answer is doing this problem in the correct order. So, assuming you know basic number operations, i.e., how to add, subtract, multiply, and divide basic numbers, the real issue here is what order to take.

[00:00:43]So, in other words, let's just take a look at this part of the problem. Should we maybe add and then divide or maybe we multiply first and then divide and then add. So, you can see here, if we take different orders, we're going to get different results and of course, there's only one order that will yield the right answer. Okay, so how do we know the correct order to do a math problem?

[00:01:07]Well, we need to understand this acronym right here called PEMDAS. So, what we're talking about here in terms of math is something called the order of operations. So, in mathematics, things like addition, subtraction, multiplication, and division and powers, these things right here are what we call mathematical operations. So, how do we know which ones to do first? Well, again, we need to reference our lovely little acronym here called PEMDAS. So, before I explain this, I'm going to go ahead and give you a nice little memory aid, a mnemonic, so you never forget PEMDAS and that is please excuse my dear Aunt Sally. One more time, please excuse my dear Aunt Sally. Now, I don't know what Aunt Sally did, but we thank her for her contributions to mathematics.

[00:01:59]All right, so PEMDAS is a checklist that goes from left to right. And here is how it works. So, P stands for parentheses.

[00:02:08]So, if we have any parentheses in our problem, that's where we're going to start. But, technically, this P stands for grouping symbols. So, you can have brackets like this or these type of squiggly brackets. In other words, grouping symbols are ways we can group numbers together. So, like right here, we're grouping all these numbers together with these parentheses right there. So, this is a bit of a hint on what we need to do first in this problem. Now, another thing about this step is if you have parentheses inside of brackets, let's say for example, you always start with the inner innermost parentheses and work your way out. Okay, now sometimes there are no parentheses in your problem and if that's the case, well, you just continue to scan this PEMDAS checklist from left to right and see if you have the next thing on the list. list and that is E and E stands for exponents, but really you can think of this as powers. So, if you have any powers in your problem, you're going to do this next. Now, let's take a look at 2 to the third power. This little number up here in the top right is called the exponent and this number down here is called the base. The entire thing is a power. So, 2 to the third power means take 2 and multiply it by itself three times. So, 2 * 2 * 2, of course, is 8 and this is how we evaluate powers. Now, again, if you don't have any powers, you just skip that step and move on to the next thing. Okay, so now we're down to M, D, A, and S and let me go ahead and just tell you what these thing these things stand for before we get into how to use this PEMDAS checklist. So, M stands for multiplication, D stands for division, A stands for addition, and S stands for subtraction. Now, it seems logical that the next thing that we need to do here is multiplication because it's the next thing on our list from left to right. Unfortunately, this is wrong and what I'm going to tell you will help you avoid one of the most common basic math mistakes out there.

[00:04:21]Now, the next thing that you do is any multiplication or division and you're going to do whatever you see first from left to right. So, in our problem here, we have both multiplication and division. Now, what should we do first? Do we do division and then multiplication or multiplication or division? Well, it all depends how you're seeing the problem.

[00:04:42]So, if you see multiplication and then division first from left to right, well, you're going to do the multiplication first, but if you have division and then multiplication and you see the division first from left to right, well, that's what you're going to do. So, you can see here, this is a major hint on how to handle this problem right here. And then lastly, when you're done with all multiplication and division, you'll finish up with any addition and subtraction and you'll handle handle it the same way from left to right. Okay, so if you understand PEMDAS, well, this is how we can solve this problem and let's take a look at these steps right now.

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[00:05:52]So, the key to solving any math problem is to take your time, be neat and organized, and show each step. So, that's what we're going to do right here and the first thing that we need to think about is PEMDAS, right? So, we have a problem with different mathematical operations. So, we need to scan our PEMDAS checklist here from left to right. So, we're going to start with P. Do we have any parentheses? Well, of course, we do. We have parentheses right here. So, that means we need to go inside of the parentheses and work on all of this math before we go outside of the parentheses. So, the next thing that we're going to do is see if we have any parentheses or grouping symbols inside of these parentheses. So, we don't have any parentheses inside of our parentheses, right? Or any parentheses inside of brackets. So, we're going to move on to the next thing and see if we have any exponents or powers. So, do we have any powers here? No, we do not. So, now we're down to multiplication and division. So, do we have multiplication and division? Yes, we do. We have division and multiplication. So, what do we see first from left to right? Well, we see division first. So, this is the first thing that we need to do. So, we're going to focus in here and do 6 / 2. Okay, so 6 / 2 is what? Well, of course, the answer is 3. So, here is our first step. Okay, we figured out that we have to do this division inside of the parentheses and the answer is 3. But, we're not done with all the math that's inside of the parentheses. So, we have 3 + 3 * 1. Now, if you think you know what to do for the rest of the problem, maybe you want to go ahead and pause the video and work on the following steps, but hopefully, you see that it's going to be pretty easy because here we have addition and here we have multiplication. So, multiplication is always going to come first before addition when we're thinking about PEMDAS. So, let's go ahead and finish this problem up. So, we have 18 divided by parentheses 3 + 3 * 1. So, we're going to do the multiplication next. All right, so again, we're not done with the parentheses. So, 3 * 1, of course, is what? Well, the answer is 3. So, 3 * 1 is 3 and now we're down to 3 + 3, which of course, is what? Well, the answer is 6. Now, notice I'm just taking one step at a time and this makes math teachers very happy, right? So, when they're reading your work, they're like, "Boy, this person understands this, this, and this. They're probably watching that guy on YouTube." Okay, so another reason to show your steps one step at a time is if you make an error not only your math teacher, but you yourself can go back and figure out where you made a mistake, right? The worst thing that you can do when it comes to doing mathematics is to skip steps and to be unorganized and sloppy.

[00:09:01]Now, I know I had a tough time being sloppy and not being so neat when I was in school, but this is something that is really important, okay? If you really want to improve in mathematics, improve in being neater and more organized and showing each step. Okay, so let's go ahead and finish this problem up. So, we have 3 + 3, of course, is 6 and now the last step is division, right? So, 18 / 6, of course, is 3.

[00:09:30]All right, so how did you do? Well, if you got this right, I definitely have to give you a nice little happy face and A+ and a 100%.

[00:09:39]So, the whole idea here is simply to review basic math skills and if you haven't done basic math in a long time, of course, you're going to lose these skills. Now, of course, all of us, you know, use our calculators and that's fine. But, it's really important that you actually understand the principles of basic mathematics. This is really important in terms of practical mathematics. Now, if you're interested in learning algebra, geometry, or more advanced math, the first thing that you need to do is make sure you have a strong math foundation, i.e. that you really understand arithmetic and basic math. So, if you want a way to improve or review in basic mathematics, let me go ahead and offer you a few quick suggestions. You'll find the links to these courses in the description of this video, but my first course that I'm going to recommend is my math foundations course. It's a quick little kind of mini boot camp, a quick review of arithmetic. All right, so I cover decimals, fractions, number operations, order of operations, positive and negative numbers, percent, etc., etc. Now, if you want to review basic math and then some algebra and geometry, check out my math skills rebuilder course. You'll find links to both of these courses in the description of this video.

[00:10:58]Okay, so with all that being said, I definitely wish you all the best in your math adventures. Thank you for your time and have a great day.