Talk:Cross-multiplication

n+2/2 -3/4=n

Why cross multiply :)

I understand how it's done, but I wish to know why it is done. By this I mean when do you use it and why does it work? I see the "long way" but I still don't understand it very well and wish for it to be expanded even further. This may also be a good question that could be answered on the article.

It is used *alot* in mathematics, physics, chemistry, and basically in everything statistically, if let's say we take the Ohm's law (physics) which can be written as: $I={\dfrac {V}{R}}$ now if R = 10 and I = 5 how does someone find V? by cross multiplying! so it becomes $V=RI=10*5=50$ this makes a lot of equations easy(ier) which is nice. 212.64.56.124 (talk) 15:44, 18 March 2008 (UTC)

You have to cross multiply because, well, number one is EASIER. Trust me, if I had to do my homework the 'real way' it would take hours showing $allthatwork.Forinstance,taketheproblem<math>{\dfrac {2}{5}}={\dfrac {x}{35}}$. To do it the real way, you would have to $5*{\dfrac {2}{5}}={\dfrac {x}{35}}*5$.</math> Then, $35*2={\dfrac {x}{35}}*35*5.$ Next, $35*2=5x$ The end result is the same as cross multiplying
Vinson (talk) 02:37, 17 April 2008 (UTC)

I think that under the use section it would benefit from an example of ratios and basic trigonometry (it saves a lot of work when using sine, cosine and tangent) as these are direct uses and probably cross multiplication is the best method for them.

It should also be noted that if ${\dfrac {a}{b}}={\dfrac {c}{d}}$ then ${\dfrac {d}{b}}={\dfrac {c}{a}}$ and ${\dfrac {a}{c}}={\dfrac {b}{d}}$ and ${\dfrac {d}{c}}={\dfrac {b}{a}}$ . The numbers are switched in a form of a cross (although the last one is obvouis as they are the inverses of the original). The proof is easy, in ${\dfrac {a}{b}}={\dfrac {c}{d}}$ multiplu both sides by d thus: ${\dfrac {ad}{b}}=c$ and ad = bc. Then devide by c. ${\dfrac {ad}{c}}=b$ snd then by d (or rather by ${\dfrac {1}{d}}$). ${\dfrac {ad}{c}}*{\dfrac {1}{d}}={\dfrac {b}{1}}*{\dfrac {1}{d}}$ ${\dfrac {a}{c}}={\dfrac {b}{d}}$

Merge

(see also Talk:Rule of three (mathematics))

Hi, the article for Rule of three (mathematics) is the same thing, and so I'm proposing a merge. Rhetth (talk) 01:13, 17 April 2008 (UTC)

I wouldn't mind seeing them merged, and perhaps improved in the process. However, when I did some research on the rule of three, I discovered, to my surprise, that rule of three typically refers only to finding an unknown term in the d position (as d used in the Cross multiply article). Before that, I thought, apparently incorrectly, that the rule of three was the way to solve for any unknown in a proportion when the other 3 terms are known. The terms cross multiplication and rule of three case are not synonymous. If the articles are merged, the usage of rule of three should be explained. Apparently, people in some trades are taught the rule of three as a procedure to be performed by rote, without an explanation of why or any reference to algebra. Finell (Talk) 03:25, 17 April 2008 (UTC)

Interesting. It would seem to me, then, that the rule of three is a type of cross multiplication? So they could stay seperate, or they could be combined under the cross multiply heading. Yet it seems to me, historically, the rule of three is a more archaic, informal method used for basic computations, where cross multiply is applicable to a broader set of problems, and so it refers to a more complicated set of problems. In that light, the rule of three may be associated with a certain historical background, like Russian peasant multiplication. Rhetth (talk)

I agree. To me, it's all algebra anyway. I started teaching my children algebra when they each started to learn arithmetic. I didn't call it that. I called it the game of "Find the Mystery Number", which we called x just for short. Since they knew to solve a + b = c for c, I showed them how to solve for the unknown in any position just by knowing the addition table. When subtraction came along, it was time to add negative numbers to the game (so any number could be used in any position), and so on. But it was always just part of the game, never studying—at least until junior high school. When they learned the quatratic formula, I showd them how to derive it for themselves by solving for x. So my two girls always loved math, although they sometimes complained that their teachers made the subject unnecessarily dull or taught procedures by rote rather than teaching how it all worked (the fun part). But to the vast majority of the population, math is something to be learned to pass tests and then forgotten. So we have the rule of three, or even cross-multiplication, as procedures for those who never really learned algebra or mathematical reasoning. Finell (Talk) 16:16, 25 April 2008 (UTC)

I would not merge them. Rule of three was well known culturally in the 19th century as extremely annoying and needs an article of its own. I am not sure that cross multiply is so significant (it has very few incoming links): perhaps it could be a subsection of something else. --Rumping (talk) 20:42, 16 May 2008 (UTC)

As far as why we cross multiply, we are simply multiplying by both denominators simultaneously. Recall that multiplication is commutative, and can be done in any order in each term (including simultaneously). The denominators end up canceling out ,when done the regular way, except on one side which is the side that you multiply by the denominator of the other fraction. Cross multiplicatoin is simply multiplying the regular way, without showing the cancelations. --98.220.191.207 (talk) 23:23, 27 May 2008 (UTC)Gravemind

I have to disagree with Rumping. both articles are short, and Rule of Three is clearly shorthand for a particular type of cross-multiplication. it could be mentioned in the merged article along with its historical usage, making a nicely sized article, and a redirect could be added so that all its current links find their way there.--Ludwigs2 (talk) 19:50, 28 May 2008 (UTC)

I'm answering the RFC. I say merge. These are essentially the same topic: Rule of Three is an application of cross-multiplying. Shalom (Hello • Peace) 19:10, 29 May 2008 (UTC)

A source that does a good job of clarifying: [1]. According to Dr. Math it would seem more pertinent to discuss the Rule of Three with more emphasis on its historic significance. Truthfully, both cross-multiplying and the rule of three are mathematically less significant as "rules" as they are simple time-savers. I don't think of either as actual mathematical rules or theorems in the traditional sense, as both are simply expedited methods of algebraic multiplication and division as has already been mentioned. In my humble opinion I would be inclined to combine both rules into one article entitled something to the effect of Solving Proportions and having both redirect. Then we would be able to incorporate the historical significance of both as the letter above cites. RShnike (talk) 02:31, 1 June 2008 (UTC)

I vote for merging. The Rule of Three should be included for historical interest only, in a separate subsection. Picardin (talk) 07:33, 13 June 2008 (UTC)

"The Rule of Three gives the answer to this problem directly; whereas in..." - the explanation for what "Rule of three" stands for and how it was solved is quite meanignless.--Mideal (talk) 12:26, 17 April 2014 (UTC)

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I think we have a consensus that the merge should occur, so I will go ahead and take care of it. if there are any further objections, of course, please state them. we can always undo the merge if necessary. --Ludwigs2 00:38, 17 June 2008 (UTC)

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He thought he saw a Garden-Door
That opened with a key:
He looked again, and found it was
A double Rule of Three:
"And all its mystery," he said,
"Is clear as day to me!"
-- Lewis Carroll
I'm not sure this counts as a reference to the Rule of Three being notoriously difficult :-)
Bruce Mardle (talk) 17:41, 14 May 2017 (UTC)

Not to be confused?

To my mind, "cross-multiply" sounds a lot like "cross product", which is of course something completely different. Might the top of this article benefit from a "Not to be confused with cross product" header? What do you think? —Preceding unsigned comment added by 209.232.210.15 (talk) 22:54, 10 June 2009 (UTC)