Order of operations
This does not apply to the binary minus operator ?; for example in Microsoft Excel while the formulas =?2^2, =-(2)^2 and =0+?2^2 return 4, the formula =0?2^2 and =?(2^2) return ?4. Mixed division and multiplication. Similarly, there can be ambiguity in the use of the slash symbol / . cgsmthood.com example 30% ‘of’ is (30/) * = 30 * 12 =
The Correct Answer Explained over 9 million views. Watch the video where I explain the correct answer. I do two main new things in this video: I illustrate the answer with binary expression trees and I relate that to how Google evaluates the expression. The Correct Answer Explained. Or keep reading. MindYourDecisions now has over 1, free articles with no ads thanks to community support!
Help out and get early access to posts with a pledge on Patreon. Most calculators will convert the parentheses into an implied multiplication, so we get. According to the order of operations, division and multiplication have the same precedence, so the correct order is to evaluate from left to right. First take 60 and divide it by 5, and then multiply by 2.
This is without argument the correct answer of how to evaluate this expression according to current usage. Some people have a different interpretation. Some people may have learned this other interpretation more recently too, but this is not the way calculators would evaluate the expression today. What would you think the author was trying to write? From this doea, the rest of the calculation works by the order of operations. First we evaluate the multiplication inside the wnat.
So we multiply 5 by 2 to get And then we divide 60 by This gives the result of 6. This is not the correct answer that calculators will evaluate; rather bodkas is what someone might have interpreted the expression according to older usage. Since some people think the answer is 24, and others think it is 6, many people argue this problem is ambiguous: it is a poorly written what is adobe photoshop cs6 portable with no single correct answer.
So if we take the expression as written, what would a calculator evaluate it as? But what does a calculator actually do? So I would argue 24 is correct by the order of operations, and it is what calculators also evaluate the expression and notice that scientific calculators are programmed to evaluate according to the order of operations. There might be some that would evaluate like the binary tree on the right hand side. For example, a textbook would have written:. This indicates that the divisor is the entire product on the right of the symbol.
In other words, the problem is evaluated:. I suspect the custom was out of practical considerations. The in-line expression would have been easier to typeset, and it takes up less space compared to writing a fraction as a numerator over a denominator:.
The in-line expression also omits the parentheses of the divisor. However, that practice of the division symbol was confusing, and it went against the order of operations. It was something of a well-accepted exception to the rule.
Today this practice is discouraged, and I have never seen a mathematician write an ambiguous how to find area of a trapezoid without height using bod,as division symbol. Textbooks always have proper parentheses, or they explain what is to be divided. If you send an email on this problem, I may not have time to reply. InSlate explained this problem and provided a bit about the history of the division symbol.
With modern typesetting we can avoid confusing expressions altogether. Lennes, N. I run the MindYourDecisions channel on YouTubewhich has over 1 million subscribers and million views. As you might expect, the whta for my books go to their listings on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
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I tried to calculate this in a scientific bosmas and the result that I get is 6. May I be wrong according to the new opinions? Skip to content. What is the correct answer to the following expression? The Correct Answer Explained Or keep reading. The correct answer is 24 according to the modern interpretation of the order of operations. Everyone is in agreement about the first step: simplify the addition inside the parentheses. Binary expression trees Since some people think the answer is 24, and others think it is 6, many people argue this problem is ambiguous: it is a poorly written expression with no single correct answer.
There are two possible binary expression trees. The Android calculator app also gives an answer of The in-line expression what is a repertory grid have been easier to typeset, and it takes up less space compared to writing a fraction as a numerator over a denominator: The in-line expression also omits the parentheses of the divisor.
About Me: Presh Talwalkar
Bodmas puzzle answers. Originally answered for “What is the correct answer of [6?2(2+1)], 1 or 9?” It is a typical divisive question, there is not a single true answer, it depends on your previos knowledge and your belief. Many people use BOMDAS, if they follow the B -. The BODMAS meaning is the same as the PEMDAS meaning — it just uses a couple different words. In this acronym, the B stands for "brackets" (what we in the US call parentheses) and the O stands for "orders" (or exponents).
Join Stack Overflow to learn, share knowledge, and build your career. Connect and share knowledge within a single location that is structured and easy to search. I'm thinking in particular of how to display pagination controls, when using a language such as C or Java. If I have x items which I want to display in chunks of y per page, how many pages will be needed? Source: Number Conversion, Roland Backhouse, AFAICS, this doesn't have the overflow bug that Brandon DuRette pointed out, and because it only uses it once, you don't need to store the recordsPerPage specially if it comes from an expensive function to fetch the value from a config file or something.
This creates a variable you don't really need, which probably has minor memory implications and is just too much typing:. This should give you what you want. You will definitely want x items divided by y items per page, the problem is when uneven numbers come up, so if there is a partial page we also want to add one page.
The integer math solution that Ian provided is nice, but suffers from an integer overflow bug. Assuming the variables are all int , the solution could be rewritten to use long math and avoid the bug:. If records is a long , the bug remains. The modulus solution does not have the bug. A variant of Nick Berardi's answer that avoids a branch:. This evaluates to 0 if r is zero or negative, -1 if r is positive. The correct solution is 0. All the integer math solutions are going to be more efficient than any of the floating point solutions.
No checks here overflow, DivideByZero , etc , feel free to add if you like. By the way, for those worried about method invocation overhead, simple functions like this might be inlined by the compiler anyways, so I don't think that's where to be concerned.
I was interested to know what the best way is to do this in C since I need to do this in a loop up to nearly k times. Solutions posted by others using Math are ranked high in the answers, but in testing I found them slow. Jarod Elliott proposed a better tactic in checking if mod produces anything. If there is a non-zero remainder then increment the integer result of the division.
The following should do rounding better than the above solutions, but at the expense of performance due to floating point calculation of 0.
You'll want to do floating point division, and then use the ceiling function, to round up the value to the next integer. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How to round up the result of integer division? Ask Question. Asked 12 years, 8 months ago.
Active 9 months ago. Viewed k times. Improve this question. Joris Schellekens 7, 1 1 gold badge 18 18 silver badges 47 47 bronze badges. Ian Nelson Ian Nelson Am I missing something?
For anyone just now finding this, this answer to a dupe question avoids unnecessary conversion to double and avoids overflow concerns in addition to providing a clear explanation.
ZX9 No, it does not avoid overflow concerns. It's exactly the same solution as Ian Nelson posted here. Add a comment. Active Oldest Votes. Improve this answer. Good job, I can't believe C doesn't have integer ceiling. Yup, here I am in mid stumbling across this great answer after trying several much more complex approaches. Show 1 more comment. Converting to floating point and back seems like a huge waste of time at the CPU level. Be aware that the two solutions do not return the same pageCount for zero records.
This simplified version will return 1 pageCount for zero records, whereas the Roland Backhouse version returns 0 pageCount. You should add parenthesis to the simplified version so that it doesn't rely on a specific order of operations. While that's not a super common occurrence, it's important to keep in mind if you're allowing users to adjust page size.
So either don't allow users to have a page size of 1, do a check on page size, or both probably preferable to avoid unexpected behavior. Show 3 more comments. For C the solution is to cast the values to a double as Math. Huppie Huppie You also need to cast the output to int because Math. Ceiling returns a double or decimal , depending on the input types. It may be inefficient but it's extremely easy to understand.
Given calculating a page count is usually done once per request any performance loss wouldn't be measurable. Nick Berardi Nick Berardi Odds are good, however, your compiler is doing that anyway.
RhysUlerich that doesn't work in c can't directly convert an int to a bool. Ajay 5, 6 6 gold badges 34 34 silver badges 52 52 bronze badges. I don't think you are realistically going to hit this bug in the scenario presented. Yes, I was being pedantic in pointing out the bug. Many bugs can exist in perpetuity without ever causing any problems. A bug of the same form existed in the JDK's implementation of binarySearch for some nine years, before someone reported it googleresearch. I guess the question is, regardless of how unlikely you are to encounter this bug, why not fix it up front?
Also, it should be noted that it's not just the number of elements that are paged that matter, it's also the page size. Mike Mike 1, 8 8 silver badges 14 14 bronze badges. This method is unlikely to be a performance bottleneck. And if it is, you should also consider the cost of the branch. DivRem dividend, divisor, out remainder ;. Nicholas Petersen Nicholas Petersen 7, 6 6 gold badges 49 49 silver badges 65 65 bronze badges. This is incorrect. For example: DivideUp 4, -2 returns 0 should be It is only correct for non-negative integers which is not clear from the answer or from the function's interface.
Thash, why don't you do something useful like add the little extra check then if the number is negative, instead of voting my answer down, and incorrectly making the blanket statement: "This is incorrect," when in fact it's just an edge case.
I already made it clear you should do other checks first: "No checks here overflow, DivideByZero, etc , feel free to add if you like. The question mentioned "I'm thinking in particular of how to display pagination controls " so negative numbers would have been out of bounds anyways. Again, just do something useful and suggest an added check if you want, it's a team effort man.
I didn't mean to be rude and I'm sorry if you take it that way. The question was "How to round up the result of integer division". The author mentioned pagination but other people may have different needs. I think it would be better if your function somehow reflected that it does not work for negative integers since it is not clear from the interface for example a differen name or argument types.
To work with negative integers,you can for example take an absolute value of the dividend and divisor and multiply the result by its sign.
Jarod Elliott Jarod Elliott IsDivisble recordsperpage? Sam Jones Sam Jones 3, 2 2 gold badges 29 29 silver badges 38 38 bronze badges. Jeremy Hadfied Jeremy Hadfied 9. Guava has a similar method Lists. Juan Mellado Richard Parsons Richard Parsons 1. Jim Watson Jim Watson 1. Kibbee Kibbee The Overflow Blog. Podcast Non-fungible Talking. Featured on Meta.
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