One of the topics taught in school that do a great job of mystifying Mathematics for young students and confuse the hell out of them is BODMAS.
So what is BODMAS?
It stands for BRACKET OPEN-DIVISION-MULTIPLICATION-ADDITION-SUBTRACTION.
What does it do? It imposes rules for a potentially ambiguous arithmetical problem.
Take this example:
4+5x3 = ?
One could say 4+5x3 = (4+5)x3 = 9+3=27.
Another could say 4+5x3 = 4+(5x3)=4+15=19.
Thus the same problem throws up two answers.
If we deem that to be a problem, then we need a solution for it.
BODMAS is the known solution. It loosely says, given an ambiguous arithmetical problem (such as the one above), you are commanded to first solve BRACKET OPEN, then division, followed by multiplication, addition and finally subtraction in that order.
This, by the BODMAS dikat, 4+5x3=4+(5x3)=4+15=19.
So the 19 answer is correct and the 23 answer is wrong.
Applause! Bravo BODMAS!!
(For the purpose of this discussion, I will leave aside BRACKET OPEN because this is not meant to be a BODMAS eulogy.
Now let us look at 4+5x3 differently.
I was begging on the street. A man gave me 4 rupees and after that 5 women were kind enough to give me 3 rupees each. I thus had 4 then 5x3 so 4+5x3=19. The way I have told the story, it is indisputable that I had 19 rupees. The confusion is about the way I wrote it.
Well, firstly, if I go through the string of numbers and operations from left to right (as is the practice), my story and the sequence match.
So 4+5x3=19.
I was begging on the street. A man gave me 4 rupees and then a woman gave me 5 rupees. Coincidentally, this happened 3 times. So I got 9 rupees thrice hence I got 27 rupees.
So 4+5x3=27.
Well you could say, but this is not OK as per BODMAS. So this couldn't have possibly happened? :-)
The point is, BODMAS claims to remove ambiguity. But why not place the onus of being unambiguous on the fella who writes the arithmetic? Just say - look use brackets so that you are sure you convey the meaning you intend. Else don't blame others for interpreting things in a way you did not intend.
So write (4+5)x3 and it is sure to be interpreted as 27 or write 4+(5x3) and be sure it is 19.
So basically BODMAS condones ambiguity and claims to resolve it. But you know, Pythagoras believed that the universe is constructed out of numbers. Some great Mathematician has said "It is evident that the Great Architect of the universe was a Mathematician". So Mathematics reflects life and vice versa. Given that we demonstrated how 4+5x3 can practically play out in two different ways, what gives anybody the divine right to lay down BODMAS as a law?
Not to mention that BODMAS confuses the hell out kids. Forget 4+5x3. Consider 12+6/9x14-4x8.
If I were a teacher I would just skip the section on BODMAS. Neither teach it not test kids on it.
By the way, other than in a chapter or section on BODMAS, BODMAS is not needed. All books, exercises and examinations are carefully presented using brackets to make the arithmetic unambiguous. Such as ((12+6)/9)*((14-4)x8)=82.
BODMAS is a solution to a non-problem. Ignore it.
Another such utterly useless topic I want to write about is SQUARE ROOT BY THE DIVISION METHOD. As of 2016 it appears in the Maharashtra SSC Board's class VII text book. I have asked by daughter to ignore it and instead resort to trial and error to find square roots of large perfect squares. Saves the child a lot of anguish and replaces it with a most interesting exercise.
So what is BODMAS?
It stands for BRACKET OPEN-DIVISION-MULTIPLICATION-ADDITION-SUBTRACTION.
What does it do? It imposes rules for a potentially ambiguous arithmetical problem.
Take this example:
4+5x3 = ?
One could say 4+5x3 = (4+5)x3 = 9+3=27.
Another could say 4+5x3 = 4+(5x3)=4+15=19.
Thus the same problem throws up two answers.
If we deem that to be a problem, then we need a solution for it.
BODMAS is the known solution. It loosely says, given an ambiguous arithmetical problem (such as the one above), you are commanded to first solve BRACKET OPEN, then division, followed by multiplication, addition and finally subtraction in that order.
This, by the BODMAS dikat, 4+5x3=4+(5x3)=4+15=19.
So the 19 answer is correct and the 23 answer is wrong.
Applause! Bravo BODMAS!!
(For the purpose of this discussion, I will leave aside BRACKET OPEN because this is not meant to be a BODMAS eulogy.
Now let us look at 4+5x3 differently.
I was begging on the street. A man gave me 4 rupees and after that 5 women were kind enough to give me 3 rupees each. I thus had 4 then 5x3 so 4+5x3=19. The way I have told the story, it is indisputable that I had 19 rupees. The confusion is about the way I wrote it.
Well, firstly, if I go through the string of numbers and operations from left to right (as is the practice), my story and the sequence match.
So 4+5x3=19.
I was begging on the street. A man gave me 4 rupees and then a woman gave me 5 rupees. Coincidentally, this happened 3 times. So I got 9 rupees thrice hence I got 27 rupees.
So 4+5x3=27.
Well you could say, but this is not OK as per BODMAS. So this couldn't have possibly happened? :-)
The point is, BODMAS claims to remove ambiguity. But why not place the onus of being unambiguous on the fella who writes the arithmetic? Just say - look use brackets so that you are sure you convey the meaning you intend. Else don't blame others for interpreting things in a way you did not intend.
So write (4+5)x3 and it is sure to be interpreted as 27 or write 4+(5x3) and be sure it is 19.
So basically BODMAS condones ambiguity and claims to resolve it. But you know, Pythagoras believed that the universe is constructed out of numbers. Some great Mathematician has said "It is evident that the Great Architect of the universe was a Mathematician". So Mathematics reflects life and vice versa. Given that we demonstrated how 4+5x3 can practically play out in two different ways, what gives anybody the divine right to lay down BODMAS as a law?
Not to mention that BODMAS confuses the hell out kids. Forget 4+5x3. Consider 12+6/9x14-4x8.
If I were a teacher I would just skip the section on BODMAS. Neither teach it not test kids on it.
By the way, other than in a chapter or section on BODMAS, BODMAS is not needed. All books, exercises and examinations are carefully presented using brackets to make the arithmetic unambiguous. Such as ((12+6)/9)*((14-4)x8)=82.
BODMAS is a solution to a non-problem. Ignore it.
Another such utterly useless topic I want to write about is SQUARE ROOT BY THE DIVISION METHOD. As of 2016 it appears in the Maharashtra SSC Board's class VII text book. I have asked by daughter to ignore it and instead resort to trial and error to find square roots of large perfect squares. Saves the child a lot of anguish and replaces it with a most interesting exercise.
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