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BigMosquito2013-01-14 15:57:47
Mathematics
BigMosquito, 2013-01-14 15:57:47

6/2(1+2) =? (a simple question on the school curriculum)

This is not humor, but simply an attempt to see the reasoning of different people on such an elementary issue.

Thanks :)

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Dolios, 2013-01-14
@Dolios

Operation precedence:
brackets
multiplication/division (left to right)
Respectively
6/2(1+2)
1. 6/2*3
2. 3*3
3. 9

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howeal, 2013-01-16
@howeal

What the fuck is this heresy in the comments? Habr is a highly educated intellectual people. They can't count. uh, no words. Didn't study at school? When there is no sign in front of the brackets, this is a multiplication. The operation in parentheses is performed first. The operations of multiplication and division are equivalent in priority.

# 6/2(1+2)=6/2*(1+2)=6/2*3=3*3=9

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Zverenish, 2013-01-14
@Zverenish

I tell you why.
Here is a picture with two options, how someone sees the final formula: Whoever thinks that the first option is correct will get 9 in the end.
Whoever thinks that the second option is correct will get 1 in the end.
But according to the rules, since 6/2 is not enclosed in brackets, it means that everything after the fraction is in the denominator, so the second option is correct.

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PaukCher, 2017-10-05
@PaukCher

First of all, I want to remind you that in the Soviet school we were taught that there is a difference between signed and unsigned multiplication. And the difference is that when multiplying without a sign, the product is treated as an integer value. At the household level, if 2a is a liter of liquid, then 2×a is two half liters of liquid.
Consider an example:
2a:2a=1
with a=1+2
2(1+2):2(1+2)= 6:2(1+2) =6:6= 1
For those who don't remember this rule , I propose to solve an example for understanding:
This example is from the "Collection of Problems in Algebra", Part I, for grades 6-7. (P.A. Larichev)
Based on the above 6:2(1+2)=1
In the manual for the mathematical faculties of pedagogical institutes on the course of methods of teaching mathematics, according to which our algebra teachers were taught in pedagogical universities of the Soviet Union, it is unequivocally stated that in algebra the multiplication sign connects the components of the action more strongly than the division sign. And the fact that the multiplication sign is omitted in the controversial example suggests that the controversial example is algebraic .
Methods of teaching algebra, Course of lectures, Shustef M. F., 1967
https://russianclassicalschool.ru/biblioteka/matem...
Text attached by me on the 43rd page of the manual.
So, for those who studied well in the Soviet school 6:2(1+2) = 1

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NiGHt_LEshiY, 2013-01-14
@NiGHt_LEshiY

www.stackoverflow.com/a/5843995/1404097

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Evgeny Elizarov, 2013-01-14
@KorP

based on the school course of mathematics of the 2nd grade - 9

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retran, 2013-01-14
@retran

nine.

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Zverenish, 2013-01-14
@Zverenish

EugeneOZ , I can’t figure out how you write the fraction horizontally in a text editor. Can you bring an example?
If we take the slash as a fraction, and the colon as a division, then here are a couple of examples.
Option 1.
6/2(1+2)
Option 2.
6:2(1+2)
If you take the slash as a division, then how to designate a fraction? Only add brackets, increasing the formula in size.
That is, 6 / (2 (1 + 2))
And when you are dealing with a bunch of brackets (in this example, there are only one nested ones - and when there are a dozen of them?) - it's easier to make a mistake. Who studied engineering at the university will understand me.

N

I first multiplied everything in brackets by 2, then divided 6 by 2 and added 4. here: 6÷2(1+2)=6÷(2*1)+(2*2)=6÷2+4= 3+4=7

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Steaze, 2017-07-07
@steaze

Oh my God, and this is a programmer's site! What the hell is "1", at least check this expression in Excel if your brains are not enough. The correct answer is "9".
Decryption: 6/2(1+2) =?
6/2*(3).
Notice, not 6/(2*3), namely 6/2*3. Calculate further for you?
It is necessary to give this task at an interview in order to weed out idiots right away.

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Zverenish, 2013-01-14
@Zverenish

one

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an_tropa, 2017-02-27
@an_tropa

The formula a*(b+c) = a*b+a*c.. And applying to the equation we get 6/2 =3 after we omit the brackets 3*1+3*2 = 9

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NikDeValero, 2017-11-06
@NikDeValero

in order to divide something, you need to get something, so multiplication in priority

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Victoria Pokrovskaya, 2019-06-27
@Pinny55

Such a proposal is easy to solve if you know the order of operations in mathematics . The correct order of arithmetic operations in mathematics depends on their type and the conditions of a particular example. Knowledge of the order of precedence is necessary, since they are the basis for both many household operations (purchases, measurements) and more complex calculations.

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AlexeyStrokin, 2019-07-08
@AlexeyStrokin

The correct answer is 9. A fraction is the division of the numerator by the denominator. But division itself is not actually a fraction.) And since a fraction is a purely horizontal line and not a division, the answer is exactly 9. Anyone who thinks otherwise is most likely relearned))).

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luftwaffel, 2019-09-22
@luftwaffel

First ":" = "/" = slash. It's all the same action. The correct answer is 9. 6:2(2+1) = 6:2*3 = 6:2 * 3:1. Multiplication of fractions. 3 will be in the denominator only in the case of 6: (2 * 3), otherwise it will be in the numerator. Who thinks otherwise - the textbook in hand.

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StrannikAl, 2021-08-11
@StrannikAl

The result
is everything is correct ATP PaukCher PaukCher for the explanations, the answer will be 1

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Shultc, 2013-01-14
@Shultc

Depending on what system of calculation you are talking about ...

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Dmitry, 2013-01-15
@Tomasina

classic: ask your neighbor "What is two plus two times two?". The results will be mixed.

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Mxmxm, 2017-08-31
@Mxmxm

and like this P

6÷2(1+2)=7 To solve this example, I use the basic rules: 1. Get rid of brackets. 2. Perform
actions according to priority. Let's consider two examples: 6÷2(1+2)=9 school program on arithmetic: release from brackets is done by operating in brackets (1+2=3) further 6÷2=3. 3x3=9. Another example: 6÷2(a+b)= where a=1. b=2. Removing parentheses by operating in parentheses (a+b=?). Another way to release parentheses is to expand the parentheses. 6÷2(a+b)=6÷2a+2b this method is used in the first example 6÷2(1+2)=6÷2+4=7. It follows that if the actions are applicable in large variants, then they are the most correct!? 6÷2(1+2)=6÷2+4=7 Thank you. Ps. For me, it's always coffee.

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Keras, 2019-02-27
@Keras

6/2(1+2) is equal to such a notation
6
-------- this is a fraction
2(1+2)
2(1+2) can be solved in two ways -
multiply 2 by brackets or solve in brackets, and then for 2
2x1+2x2=6 2x(1+2=3)=6 the answer is the same
6/6
or 6
-
6
no matter how you divide it will still be 1!!!!

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Why_Me, 2019-09-23
@Why_Me

I'll make a point or something. The problem stems from a mathematical inaccuracy when writing division "in a column" when using a horizontal bar. After all, if in the example we rewrite 6 in the numerator, and everything else in the denominator, no one will have any doubts. The answer will be unequivocally 1 and it will be the correct answer.
Now, let's say our task is to cram our example into a string. Obviously, there are no vertical lines for a computer. Let's also assume that we are not very careful and just stupidly replace the line with division, i.e. "/" or "*" depending on the parser. We count in any calculator and with some probability (depending on the answer to the topic's question by the developer of the calculator) we get 9. And this is also the correct answer.
We get 2 different correct results for, as we are sure, an identical expression. And the problem is actually that the expressions in these cases are not identical. I remind you about the order of operations: brackets, multiplication (the same as division), sum. And when we write a fraction with a vertical bar, brackets are implicitly superimposed on the numerator and denominator, and a division sign is placed between them. And for some reason, everyone remembers about the division sign when they get rid of the line, but they forget about the brackets. Or they deliberately invest in the "slash" the meaning of a vertical bar. But there is no single standard for the slash, someone interprets it as a division sign, and someone as a division sign with brackets for the numerator with a denominator. Another problem is that sometimes they are interchangeable, but this is not a general case, which many people forget.
In other words:
1) a/b != a:b
2) a/b == (a):(b)
From which by the way it follows that 2*2+2 != (2)*(2+2).

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Eptiy, 2020-06-19
@Eptiy

Here it is worth clarifying what the "/" sign means for you. Usually it means a fraction, i.e. 6/2(1+2)=6:(2*(1+2)). If we judge like this, then the answer is 1. You can argue as much as you like, but if you just turn to the source: "/" - slash (fraction), ":" - divide (division), then everything will immediately become clear.
PS The fraction sign differs from the division sign in that it has priority over the latter, the same priority as the division sign has over the subtraction sign. To make it easier to understand, I will give an example of a degree. If the answer to the expression "2:2*2" is "2", because operations are performed in order (division and multiplication have equal priorities, no brackets), then the answer to the expression "2:2^2" will be "0.5" (the sign of the degree has priority over multiplication / division, there are no brackets); while separately that "2 * 2", that "2 ^ 2" will be equal to "4". The question becomes even clearer if we remember that the fraction and degree are interchangeable ("2^(-1)=1/2", "2^1= 2/1", both examples are vice versa).

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Anton_Aly, 2021-10-22
@Anton_Aly

The ÷ sign is sometimes used to indicate a range, in which case the answer is 6

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agent_network, 2022-03-26
@agent_network

It all depends on whether we are selling or buying?
If I sell, then I will assume that the price is 9
And if I buy, then I will assume that the price is 1

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