Simple Primary Maths Question
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A primary school student asks these questions :
Why do we need to change the divide sign into multiply sign when we divide fractions ?
Why do we need to overturn the fraction behind the divide sign when we divide fractions ?
Example
3/4 divided by 5/8
= 3/4 multiplied by 8/5
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the primary school has a maths primary teacher.
Go ask.
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So that you can get the correct answer and pass your exam.
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I thought Lee012Lee was a genius.
How come you don't know this simple logic?
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So, you know the logic huh ?
Maurizio13 is a genius, Lee012Lee is not a genius lah.
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I am not genius, you are just subnormal.
This is common knowledge.
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So, you just do division of fractions without knowing why you need to change the divide sign to multiply sign and you just overturn the fraction behind the divide sign without knowing the reason for doing so lor
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Ok, ok. I explain simple simple.
Take a simple fraction like 1/2 and divide it into 1/2.
How you get 1/4?
You need to draw half a cake and divide that half a cake by half.
Voila, 1/4 cake.
And how you get 1/4 cake is by changing signs.
I am sure a math major graduate can explain in technical terms to you, but mine is the simple simple primary school math explanation.
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Ya lor,
Example
8 sweets are shared by 4 boys. Each boy get 8 divided by 4 = 2 sweets per boy
ie 8 divided by 4 = 2
Alternatively,
Since there are 4 boys, each boy will get 1/4 share of the 8 sweets = 2 sweets per boy
ie 8 multiplied by 1/4 = 2
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Charlie: Hey Benny, have you eaten? Oh you have.
Benny: ?!
You answer your own question, for !@#$ ?
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Hmm, allow me to share some of my own opinions which may not differ alot from you people...just more concise, and may be easier to explain to a primary school student. Not guaranteed though!
Imagine you have 1 piece of something. Now, for the sake of argument, you are to divide by 1/2 piece. Which means to ask how many 1/2 pieces are there in 1 piece. Since 1/2 piece is 1 piece split into 2 equal and smaller pieces, there 2 of the 1/2 pieces present in 1 piece. One can use this argument to generalise and get:
1 (divide) 1/n = n (1.1)
Then, you can multiply by a factor of m, which means to say to add 1 by m times. Since in 1 piece there are n number of 1/n, in m pieces there are mn number of 1/n pieces and so,
m (divide) 1/n = mn (1.2)
Clearly, the statement is numerically equvilent to saying having 1 piece divided by 1/mn. Which can be easily seen from equation (1.1). Intuitively, since n is added m times, the number of pieces to split up is increased by m times.
1 (divide) 1/mn = mn (1.3)
Next if 1 piece is split into p/n, which means 1/n added p times, then
1 (divide) p/n = n/p (1.4)
Intuitively, when you count n pieces of 1/n you get 1 piece, and p/n is already the value when you count p times of 1/n. So now when you count n times, you get p pieces instead. So to get 1 piece, you have to divide by p times now.
Putting these ideas together and you see that the general rule of thumb is that you have to overturn the fraction after the division sign!
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Originally posted by Audioboxing:
Hmm, allow me to share some of my own opinions which may not differ alot from you people...just more concise, and may be easier to explain to a primary school student. Not guaranteed though!
Imagine you have 1 piece of something. Now, for the sake of argument, you are to divide by 1/2 piece. Which means to ask how many 1/2 pieces are there in 1 piece. Since 1/2 piece is 1 piece split into 2 equal and smaller pieces, there 2 of the 1/2 pieces present in 1 piece. One can use this argument to generalise and get:
1 (divide) 1/n = n (1.1)
Then, you can multiply by a factor of m, which means to say to add 1 by m times. Since in 1 piece there are n number of 1/n, in m pieces there are mn number of 1/n pieces and so,
m (divide) 1/n = mn (1.2)
Clearly, the statement is numerically equvilent to saying having 1 piece divided by 1/mn. Which can be easily seen from equation (1.1). Intuitively, since n is added m times, the number of pieces to split up is increased by m times.
1 (divide) 1/mn = mn (1.3)
Next if 1 piece is split into p/n, which means 1/n added p times, then
1 (divide) p/n = n/p (1.4)
Intuitively, when you count n pieces of 1/n you get 1 piece, and p/n is already the value when you count p times of 1/n. So now when you count n times, you get p pieces instead. So to get 1 piece, you have to divide by p times now.
Putting these ideas together and you see that the general rule of thumb is that you have to overturn the fraction after the division sign!
You want to explain all this to a primary school kid?