# Asking for opinions about a mathematical fact. Why multiplying by zero equals zero? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [September 20, 2024, 4:02am UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506 "2024-09-20T04:02:19Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [September 20, 2024, 3:49pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/41 "2024-09-20T15:49:08Z")
> [@Robot\_Arm](#): > > I remember some things that confused me when I was a kid. There were ideas that I wasn’t able to articulate. Then it was the job of your teachers to get that out of you and understand your learning style. If they failed to do so, that is not your fault, and there is nothing wrong with your brain. Anyone who can be reasonably literate and write well, as you and Stoid quite obviously can, can also learn the fairly simple language of rudimentary arithmetic. > [@Saint\_Cad](#): > > I agree that many elementary teachers are poor at teaching math, but as a math teacher it is offensive that you IMMEDIATELY assume it is the teacher’s fault. “Fault” is not the point here. Sorry, but this isn’t a matter of personality. It’s just observed fact. It is the job of elementary school to instruct children in arithmetic, and in some cases that job is not done adequately. All children who do not have severe learning disabilities are capable of understanding arithmetic, and so if they are not taught it, the teachers failed. That may not be the teachers’ FAULT. Perhaps they were not equipped with the right tools, or the class size was so large there was insufficient time to attend to the child’s particular needs. It may be a lack of parental support. It may not be a problem with the teacher’s competence. Or it may be. Every case is different. It is a simple a factual observation that a child quite capable of understanding basic math - we aren’t talking about calculus - was not effectively helped to achieve that understanding. The job was not done. The reason it was not done will vary from case to case, but in most cases the reason is NOT that kids like Stoid were incapable of learning it. We have thousands, maybe millions, of adults now walking around thinking they’re stupid in a pretty important area of life, and they’re just not. Given that you are actually a MATH teacher, I doubt you’re ever the problem. Teachers specializing in math are, after all, specifically trained and experienced at teaching math. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [September 20, 2024, 4:12pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/42 "2024-09-20T16:12:57Z")
> [@RickJay](#): > > “Fault” is not the point here. Sorry, but this isn’t a matter of personality. It’s just observed fact. It is the job of elementary school to instruct children in arithmetic, and in some cases that job is not done adequately. All children who do not have severe learning disabilities are capable of understanding arithmetic, and so if they are not taught it, the teachers failed. You leave out the possibility that the student says, “I’m bad at math so fuck it.” and those around them agree and give them a pass for refusing to make an effort to learn. I’ve seen that as many times as I’ve seen elementary teachers being bad at teaching math. > [@RickJay](#): > > and so if they are not taught it, the teachers failed. And so if they do not learn it, the student failed? > [@RickJay](#): > > The reason it was not done will vary from case to case, but in most cases the reason is NOT that kids like Stoid were incapable of learning it. Re-emphasizing that most students are capable of learning math, but many refuse to because, “Math is hard.” And if you are going to blame the teachers for giving them a pass for not learning it, then you also need to call out their parents, society and even the students themselves. Oh and throw in school administrators too. > [@RickJay](#): > > We have thousands, maybe millions, of adults now walking around thinking they’re stupid in a pretty important area of life, and they’re just not. But yet they claim they are and that they are incapable of learning it and everyone around them reinforce this by saying “Me too.” or “Math is tough.” or “Yeah, teachers suck.” I mean look at the OP. > [@Stoid](#): > > I am a math moron. Numbers just twist my brain into knots and have since they tried to reach me how to multiply in 3rd grade. ( > [@Stoid](#): > > You are unfamiliar with the word “moron”, I see. I am one. I was in remedial math for my entire school career, starting in 4th grade. That is a classic example of the fixed mindset if there were ever one. Again, I don’t disagree that in many or most cases there is a problem with how math is taught in elementay school … in fact I agree with that assessment. BUT the two quotes I pulled out is what I hear from parents all the time viz. “My child not being successful is your fault because you are incompetent and my precious little angel always does his best and you are the devil blocking his education.” No responsibility on the student to make an effort to learn. Learning is an **active** process. > [@RickJay](#): > > Anyone who can be reasonably literate and write well, as you and Stoid quite obviously can, can also learn the fairly simple language of rudimentary arithmetic. > [@Stoid](#): > > I think, based on later self education, that what you’re doing is sort of algebraic and **I don’t do algebra.** Emphasis added So it is my fault that they dig their heels because “they don’t do algebra”? ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [September 20, 2024, 6:06pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/43 "2024-09-20T18:06:42Z")
> [@Saint\_Cad](#): > > But yet they claim they are and that they are incapable of learning it and everyone around them reinforce this by saying “Me too.” or “Math is tough.” or “Yeah, teachers suck.” I mean look at the OP. Well… yes, I looked at the OP, that’s what I have been responding to. > [@Saint\_Cad](#): > > You leave out the possibility that the student says, “I’m bad at math so fuck it.” That is a possibility, but I’m sorry, I don’t buy it’s a common one among **seven-year-olds**. We’re not talking about something that usually crops up in high school, we’re talking about a problem that almost invariably starts when the child is quite small, and it compounds from there, because if you haven’t adequately learned key things in an early grade, you’re in trouble the following year. A first or second grader is at an age when they must be led through this. They are not going to permanently shut down because they had a tough Wednesday. > [@Saint\_Cad](#): > > So it is my fault that they dig their heels because “they don’t do algebra”? I’m sorry, but I already addressed this; it is not a matter of whose “fault” it is. We are not discussing you personally, and I am not interested in assigning “fault.” It could be the failure of actions or lack of action by many parties - as, again, I very clearly stated. This is not a matter of blaming people or casting aspersions on a person. It is a matter of simply observation that the job of the school is to teach basic things, and the school has failed to do so if the child does not learn a basic thing when the child is capable of doing so. I am stating a fact: essentially all children can be taught functional, basic math. If they are not taught basic math, then they were not adequately taught. How to fix that is a much bigger discussion. There is nothing wrong with the children’s brains. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [September 20, 2024, 6:18pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/44 "2024-09-20T18:18:58Z")
> [@RickJay](#): > > That is a possibility, but I’m sorry, I don’t buy it’s a common one among **seven-year-olds**. It is. Usually because an innocent statement like, “This math sheet is hard.” is reinforced by all around them that yes it is. We (society) teach students at a young age that it is acceptable to fail/be bad at math. > [@RickJay](#): > > I’m sorry, but I already addressed this; it is not a matter of whose “fault” it is. Whatever you want to call it, you said that they were poorly taught. Chingon was more explicit that it is on the teacher. However you want to put it, teaching and learning are not reciprocals of each other. They could have had the best 2nd grade teacher in the world and on the student side they did not learn the math for a multitude of reasons. What if stoid had horrible attendance that year of elementary school. How was he poorly taught? That phrasing puts it on the teacher and the school. Let me ask you this. Is it possible that stoid’s inability in math comes from establishing in his formative years a fixed mindset that he is bad at math and there’s not a goddamn thing they can do about it? ---
**Author:** ![Robot\_Arm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robot_arm/32/18280_2.png) [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)\ **Post date:** [September 20, 2024, 8:03pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/45 "2024-09-20T20:03:16Z")
> [@RickJay](#): > > Then it was the job of your teachers to get that out of you and understand your learning style. If they failed to do so, that is not your fault, and there is nothing wrong with your brain. Actually, the cases I was thinking of had nothing to do with math, or with school subjects at all. They were idioms that I couldn’t interpret the first few times I heard them. I remember being confused, but not able to explain exactly why; msuch as the OP sounds. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [September 20, 2024, 9:26pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/46 "2024-09-20T21:26:32Z")
It probably won’t help, but frisbees aren’t numbers. Anyway, 0\times x=(0+0)\times x=0\times x+0\times x and cancelling 0\times x from both sides leaves nothing (that is 0 on the left side and 0\times x on the right. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [September 20, 2024, 9:27pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/47 "2024-09-20T21:27:02Z")
> [@Saint\_Cad](#): > > Let me ask you this. Is it possible that stoid’s inability in math comes from establishing in his formative years a fixed mindset that he is bad at math and there’s not a goddamn thing they can do about it? I thought Stoid was a she? That is possible, but rather exceedingly unlikely. Anything is _possible_, but many things are very unlikely. A small child can be guided through that. I’ll go with the 99 percent likelihood every time. ---
**Author:** ![Chingon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chingon/32/17645_2.png) [@Chingon](https://boards.straightdope.com/u/Chingon)\ **Post date:** [September 20, 2024, 10:52pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/48 "2024-09-20T22:52:48Z")
> [@Saint\_Cad](#): > > Chingon was more explicit that it is on the teacher. I was trying not to be rude to the OP. Of course I wouldn’t blame a child for not getting this concept. They don’t have that level of control over their education. A math teacher who passed such a child did them a great disservice (and the parent who probably forced them to is equally culpable). An adult who still refuses to try to understand multiplication is of course likely pushing an affectation. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [September 20, 2024, 11:05pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/49 "2024-09-20T23:05:23Z")
> [@Hari\_Seldon](#): > > It probably won’t help, but frisbees aren’t numbers. Anyway, > 0\times x=(0+0)\times x=0\times x+0\times x > and cancelling 0\times x from both sides leaves nothing (that is 0 on the left side and 0\times x on the right. I had not replied to this thread, but, despite the OP insisting that he or she was a mathematical “moron”, said that they had a sense for algebra, and what the question is about is an algebraic fact. So all the stuff about frisbees may end up more confusing than the proof quoted above, and is not directly relevant anyway. ---
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [September 20, 2024, 11:20pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/50 "2024-09-20T23:20:08Z")
I think of it like a kids joke. Answer this question and I’ll give you ten times what’s in my pockets. They answer correctly. 😀_how much did I get_? You show them your empty pockets. I can only understand it from the viewpoint of multiplying whatever I have. You can multiply zero by any amount and the result is zero. That’s how my grade school math teacher explained it. You can think about why division by zero is undefined. Use a calculator and divide 345 by 1.5 Then divide 345 by .15 and again divide 345 by .00015 The answer gets huge as you approach zero. Studying that is week one of Calculus. It’s how they introduce Integrals. ---
**Author:** ![Atamasama](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/atamasama/32/12961_2.png) [@Atamasama](https://boards.straightdope.com/u/Atamasama)\ **Post date:** [September 20, 2024, 11:28pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/51 "2024-09-20T23:28:31Z")
> [@Stoid](#): > > If I have one frisbee, a real frisbee that I can hold in my hand and tell you what color it is and throw it… And I multiply that frisbee by zero… Mathematically, I now have no frisbees at all. Even though I started with one. (Obviously, in the real world I still have that frisbee. So why does math take it away from me?) > > How come? I know I answered you in the other thread, but I think I might have a way for this to make sense. Think of it this way, the term “multiply by zero” is just another way of saying “take it away”. **That’s literally all it means.** Think of math as another language, like Chinese or Latin. The phrase in Mathematics that says “multiply by zero” just means “take it away” in English. So, let me repeat what you said, but translate the Mathematics into English (which is the bolded part). > If I have one frisbee, a real frisbee that I can hold in my hand and tell you what color it is and throw it… And **that frisbee is taken away from me** … Mathematically, I now have no frisbees at all. Even though I started with one. Does that make sense now? It’s just a way to represent in math the act of completely removing something. That’s why multiplying anything by zero leaves you with zero. Because tautologically, you’re saying that when you take everything away, you are left with nothing. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [September 20, 2024, 11:37pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/52 "2024-09-20T23:37:48Z")
I learned in school that “zero” was a number such that 0+x = x+0 = x for any number x. Maybe that takes some effort to grok (if it did not, why was zero not considered a genuine number in so many times and places?) but once you accept it, it certainly follows that any number times zero equals zero. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [September 20, 2024, 11:42pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/53 "2024-09-20T23:42:01Z")
> [@filmore](#): > > By the way, you’re not alone in being confused about zero. Zero is weird. You can think of it both as a number and as a concept. It took mathematicians a long time to come up with zero. It was a concept not known to many societies. The cool thing about zero and infinity is that although they’re special numbers that can’t be used in the ordinary way in most calculations, they actually have value in producing useful results in contexts like limits in infinite summations. Thus it’s perfectly reasonable to speak of the limit reached (for example) by an infinite series as the value of the terms **approaches** zero and the number of terms **approaches** infinity, even though zero and infinity themselves are meaningless here. You can approximate the area under a curve, for instance, by drawing a series of rectangles and summing their areas. The narrower the rectangles, and the more of them there are, the more accurate your answer will be. Given the function defining the curve, I’ve always been fascinated by the fact that you can compute the exactly precise sum that the areas of the rectangles approaches as their width approaches zero and their number approaches infinity. So, remarkably, “zero” and “infinity” are very practical concepts! 🙂 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 20, 2024, 11:46pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/54 "2024-09-20T23:46:49Z")
> [@bleach](#): > > What might be tripping you up is that you are starting with something, a frisbee. And then Evil Math takes it away when you do a perfectly legit multiplication. But that line of thinking doesn’t make sense for any mathematical operation. If I have one frisbee, I can’t just say “Multiply it by five” and suddenly have four more frisbees appear out of thin air. Math doesn’t make things happen in the real world; it just describes things that are already happening in the real world. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [September 20, 2024, 11:54pm UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/55 "2024-09-20T23:54:55Z")
A mathemagician did it. ---
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [September 21, 2024, 12:04am UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/56 "2024-09-21T00:04:01Z")
Quick correction from my post. _derivatives_ It’s been 37 years since my calculus classes. Doesn’t matter here. I was making the point that zero has many special properties. Zero is the intersection of x and y on a graph (Cartesian coordinate system) Students in science classes take measurements during an experiment. The teacher has them turn in a graph for homework. It’s how the results of an experiment can be visualized. Zero is a cool number. Multiplying anything by zero equals zero is just a special property of the number. ---
**Author:** ![Ranger\_Jeff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ranger_jeff/32/2065_2.png) [@Ranger\_Jeff](https://boards.straightdope.com/u/Ranger_Jeff)\ **Post date:** [September 21, 2024, 2:11am UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/57 "2024-09-21T02:11:06Z")
The HP-15C is THE ULTIMATE in pocket sized programmable RPN calculators. The 11 has a little less memory and doesn’t come with a built in program for matrix algebra. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [September 21, 2024, 5:02am UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/58 "2024-09-21T05:02:08Z")
Ok, so here’s a question about your physical frisbee. What happens to it when you multiply by -1? ---
**Author:** ![Robot\_Arm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robot_arm/32/18280_2.png) [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)\ **Post date:** [September 21, 2024, 5:18am UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/59 "2024-09-21T05:18:39Z")
> [@Chronos](#): > > Math doesn’t make things happen in the real world; it just describes things that are already happening in the real world. Yeah, that’s well put. A methematical equation is not an incantation that causes something to happen. An equation is a way of describing (or “modeling”, if you prefer) something in the real world, and then you can use the rules of math to draw conclusions about it. > [@aceplace57](#): > > Zero is a cool number. Zero is my hero. > [@Ranger\_Jeff](#): > > The HP-15C is THE ULTIMATE in pocket sized programmable RPN calculators. I still have mine from college, and use it. Woe unto he who tries to take it from me. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [September 21, 2024, 9:45am UTC](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506/60 "2024-09-21T09:45:43Z")
> [@Snarky\_Kong](#): > > Ok, so here’s a question about your physical frisbee. What happens to it when you multiply by -1? That was already answered, but to phrase it differently, multiplying anything by a negative number is exactly the same as multiplying by a positive number, except that the result goes on the “debit” side of the ledger. IOW, if you have -1 frisbees, you have an obligation to go out and get 1 frisbee and then give it to your creditor so you now have 0 frisbees. Negative balances are very much a thing in the real world – they’re called debts. [Previous page](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506.md?page=2) [Next page](https://boards.straightdope.com/t/asking-for-opinions-about-a-mathematical-fact-why-multiplying-by-zero-equals-zero/1007506.md?page=4)