4 ÷ (3 – 5) × 2 = ? This Simple Math Problem Stumps A LOT of PEOPLE! Can You Solve?

Added: 2026-05-13

[00:00:00]So, can you solve this basic math problem without the aid of a calculator?

[00:00:06]Well, a lot of you are going to get this wrong. And it's not because you don't understand how to multiply, divide, add, and subtract numbers. It's because you don't understand this acronym right here, PEMDOS, which is all about something called the order of operations. Now, most math teachers, math courses, and math books use this acronym, PEMDOS, to teach the order of operations. There are uh other acronyms but but uh PEMDOS is by far the most common. All right, so let's see how you do with this problem. Again, the only rule here is no calculator. And the problem is 4 / parentheses 3 - 5 partheses * 2. What is the correct answer? Well, go ahead and put that into the comment section. I'm going to show you the right answer in just one second, and then I'm going to walk through the solution to this problem step by step so you understand the correct order of operations. This uh is probably one of the most common uh places where uh students make errors in mathematics. So you definitely want to pay attention to what I have to say in this video. Okay.

[00:01:09]So let's go and take a look at the right answer. The correct answer is one of these numbers right here. Now obviously one number is right and the other number is wrong. And there could be obviously infinite uh infinite amount of wrong answers. But uh probably the most common wrong answer is one of these numbers.

[00:01:29]Okay, so that's why I have it here. So if you see your answer that is fantastic. So somebody did this right and somebody did this wrong. Okay, so let's go ahead and identify the correct answer. So if you answered with negative 1, you did that wrong. The correct answer is indeed -4. All right. So, for those of you that did um come up with negative one, you probably made the most common uh mistake when it comes to the order of operations. And I'm glad you made that mistake because this uh video is going to straighten out this confusion. And from this point forward, you're going to be looking like this person. But, uh if you got this right, we have to give you an A+, a 100% and multiple stars. you could brag to your friends and family that indeed you are a certified professional expert in the area of order of operations and uh PEMDOS. All right, so let's go and get into the solution right now. So here is our problem and uh we need to understand something and that is what is a mathematical operation. I'm saying the order of operations. But in mathematics, these things like this addition, subtraction, multiplication, division, and even uh powers. These are things we can do with numbers. And these uh things right here specifically are mathematical operators. Okay? So, we're talking about mathematical operations. And when we have a problem that has more than one type of operation, we need to know the correct order to do the prompt. Because if we uh just kind of randomly say, you know what, I want to kind of do multiplication first and then I'll do addition, then maybe I'll go to division, then back to multiplication.

[00:03:07]Well, depending on the uh the order you take, okay, you can come up with all different sorts of values. Of course, there's only one correct uh order, and that order is this acronym right here.

[00:03:20]This is effectively a checklist for us, and I'm going to go ahead and explain this right now. All right. So this checklist PEMDOS works from left to right. And these letters stand for something. And before I explain to you what these letters stand for. Okay, let me give you a little memory aid here.

[00:03:37]And that is please excuse my dear aunt Sally. Uh please excuse my dear aunt Sally. This uh phrase and acronym has been around for years. Probably my great great grandparents were saying this way back in the good old days. But anyways, let's go ahead and get into uh the correct order of operations right now.

[00:03:56]All right, so P, what does P stand for?

[00:03:59]P stands for parentheses. Okay, and obviously we have some parenthesis here.

[00:04:03]But P also stands for brackets or these kind of little squiggly brackets like this. Uh really P stands for grouping symbols. Okay, so if you see numbers grouped together by parenthesis, brackets or squiggly brackets, this is where we start. Now something uh about uh parenthesis. If you have multiple sets of parentheses, you want to work from the innermost parentheses first.

[00:04:27]Okay. All right. So, we don't have that situation, but we definitely have parenthesis. Now, let's move on to our next letter, which is E. Now, E stands for powers. So, you might be saying, "Hey, Mr. YouTube Math man, you're saying powers, but uh this is E. Why doesn't you know, how come we don't have a P here if you're saying powers?" Well, when we look at a power, something like 2 to the3 power, this little number up here to the top right is something called an exponent. This big number down here is called the base. And this entire thing is referred to as the power. So, e really stands for exponents, but you can think of it as uh powers. Okay? So here is the most common uh place of confusion when it comes to the order of operations and it's what these letters right here uh particularly M and D. All right. So before I tell you that let's just make sure you understand what MD, A and S stand for. M is multiplication, D is division. A is addition. S is subtraction. All right. Now, most of you might be, you know, thinking, well, if this is a checklist that goes from left to right, and this is where most people get themselves in trouble with with the order of operations. It's a checklist that goes from left to right. So, I have to do multiplication first every single time. If I have both multiplication and division in a problem, I got to do all the multiplication, then I move on to division, and then after that, I go on to addition and subtraction. This is not the way this works. Okay? And I don't think that uh uh if you got this wrong, I think a lot of um textbooks and uh maybe some teachers don't emphasize this as much because again this is a highly confused area. So let's go ahead and talk about how it actually works. Okay, so M and D and ANS are actually groups.

[00:06:13]So what you're going to do here with multiplication and division is you're going to do uh multiplication or division whatever you see first from left to right. In other words, if I see division and then multiplication, I'm going to do it this way. So my acronym could be DM. But if I have multiplication and then division, I'll do it this way. So you have to consider what's going on from left to right. And addition and subtraction work the same way. All right. So, uh this again is one of the the most commonly uh confused parts of the order of operations. And if you confuse this, this is why you came up with that negative one answer. Um if you a matter of fact, let's just go back here. If you yes, if indeed if you got negative one as your answer, it's probably because you confuse this part.

[00:07:05]But that's going to be easy to fix.

[00:07:07]Hopefully, you're like, "Oh, okay. I see where I made my mistake." And that's fantastic. Okay, let's go ahead and finish this problem up. Uh, of course, now that I explained the correct order of operations, if you didn't know it, maybe you want to go ahead and try this problem all over again. All right, so let's go ahead and get started. So, what do we do first? Well, we are thinking to ourselves, uh, PEMDAS, right? This guy is saying PEMDAS. What do I do first?

[00:07:32]It's just a checklist, right? So, you ask yourself, do I have any parentheses?

[00:07:36]Yes, indeed. I have parentheses right here. So, this is where we have to focus. Okay, we have to do this step. Uh first you have 3 minus 5. Now if you don't know your positive and negative numbers, well then you may not have known the answer here. But uh if you um didn't understand that 3 - 5 is -2 because that is the correct answer. Uh you might want to review some basic math. Let me give you a quick suggestion. You might want to check out my math foundations course. It's just a basic uh kind of math boot camp. It's a small course. You'll find a link to it in the description below. But anyways, 3 - 5 is -2. All right, so 3 - 5 is the same thing as 3 + -5. All right, so hopefully you understand that. So this now is our problem. Okay, we have 4 / -2 * pos2. Okay, so what's the next step?

[00:08:30]Well, this is where we have to be thinking about our PEMDOS again, right?

[00:08:35]So okay, did I do uh everything in parentheses? Yes. Now, although there's parentheses right here, there's nothing left to do inside the parentheses. So, this step is effectively done. Okay. E.

[00:08:46]Do I have any powers? Nope. I don't have any powers. No exponents there. Do I have multiplication and division? Yes, I do. Okay. What do I see first from left to right? Well, I see division before multiplication. So, this is what we need to do first. Okay. Now, if you looked at PEMDAS, you're like, "Okay, I got to do multiplication next and then division."

[00:09:11]You would have done that. Okay? And of course, you would end up with -1. All right? So, let's go and finish this problem up. So, here we're going to be doing division, right? Because we just talked about that. This is what we see first from left to right. So, 4 / -2, we're going to get that answer. Then multiply by two. Not much work to do here because we're just talking about basic division and multiplication. So 4 / -2 positive uh a positive number divided by a negative number is negative. So that's going to be -2 * a positive2 which will give us -4 as the correct answer. But let's just do this problem wrong here. Okay, let's say we're just following the order of operations, you know, uh PEMDOS the way we think we understand it. Okay, and again I've been doing this for decades and decades and most students are just kind of quickly going through this checklist. All right, I did parenthesis.

[00:10:02]There's no powers. Now I'm going to do multiplication. So they just go right here. So if you were to do this, you would have what? Uh 4 / -2 * 2. This is going to give us, let me do it right here. 4 / -2 * 2, that's -4. So 4 /4 will give us a -1, which of course is not the correct answer of -4. That's why we have uh the order of operations. But, you know, don't feel bad if you got this problem wrong because again, this is a highly confused area. And this is why I make these uh videos. Okay? I actually um have made quite a few videos on this particular topic. No, one of the quick comment too. Some people there is a little bit of a debate about, oh, you don't have to follow PEMDAS that that's not true. Well, I'm going to tell you right now, okay? 99.9999% of math uh books, math teachers teach and use the order of operations as described by PEMDAS. If you use your calculator, okay, something like a TI um 30 or any kind of scientific calculator, guess what? Your calculator is going to follow this order of operations. So you know um of course I don't want to uh deter you from believing something other than you know what you want to believe but when it comes to mathematics in terms of what's taught you know middle school, high school, college, you got to know the correct order of operations as defined by PEMDOS. Okay. So uh for those of you that do need additional help in this, I have tons of videos on my YouTube channel. Also uh a couple courses um that you can check out. I'll leave links to those in the description.

[00:11:40]One is my math foundations course if you want to just review basic math. If you really want to relearn a lot of math, check out my math skills rebuilder course. That's a new course of mine.

[00:11:50]Teach a lot of um basic math, algebra, and geometry. And then I have all my main courses like pre-alggebra, algebra, and algebra 2. You can check those out as well. Okay. So, with all that being said, I definitely wish you all the best in your mathematics adventures. Thank you for your time and have a great day.