How Many Pieces?
You are tasked to divide 46 apples evenly amongst 86 students. What is the minimum number of pieces required to complete this task?
The answer is 130.
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1 solution
Moderator note:
Why does this formula work?
Try your formula with 7 apples divided amongst 18 people.
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24 eh?
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Work it out without the formula.
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@Guiseppi Butel – I don't know....Would you please help?
We could give 4 3 2 3 to 86 students.....Then what?
We are rest with 4 3 2 0 piece.
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@Anandhu Raj – Follow my solution in "A bunch of apples". If you still have a problem I am willing to assist you.
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@Guiseppi Butel – Thanks sir.:)
@Guiseppi Butel – I don't see how is this evenly divided, It looks like I need to build up my knowledge regarding this topic\kind of problems; so would you please guide me to a reference or a point as to where should I start, thanks in advance
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@Ahmed Obaiedallah – Start off with a simpler problem.
Suppose you had to divide 2 apples evenly amongst 3 people. What is the least number of pieces required to complete the task?
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@Guiseppi Butel – thank you both for the advice and the quick response, I think my problem is I didn't and still can't understand the question, like what does the word pieces refer to
(is it an additional number of apples to be added which will help me to evenly distribute the apples amongst the targeted people)
or
( does it mean the number of slices I have to cut so it would be suitable to distribute it among those people) and if it refers to the number of slices does it mean the total number of slices or the slices of each apple
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@Ahmed Obaiedallah – In solving the simpler problem that I had proposed I would cut each apple so that one piece would equal 2/3 of an apple and the other piece would equal 1/3 of an apple. Then I would give a 2/3 piece to one person, a 2/3 piece to another person and 2 1/3 pieces to the third person. Hence each person would get the equivalent of 2/3 of an apple. The number of pieces would be 4.
I hope this clears the intent of the problem.
If it does then try a more difficult problem.
Suppose you had to divide 3 apples evenly amongst 5 people. What is the least number of pieces required to complete the task?
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@Guiseppi Butel – ahhh I see .. now that's very clear,thank you very much for explanation and for your time
ok let's try to solve the example it will be 7 pieces .. I'll cut one apple into 5 3 and 2 5 1 and the other two apples will be cut into 5 3 and 5 2
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I left a comment in the "A bunch of apples" discussion outlining my approach to the 7/18 scenario. I find that the formula works in that case too. Did you find a value less than 2 4 ?
Here's a shortcut formula = 4 6 + 8 6 − g c d ( 4 6 , 8 6 )