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Division question

  1. Oct 24, 2004 #1
    HI

    please can someone help me with this quick question on division :

    If I have to do 3 divided by 4
    ____
    4 |3


    4 doesn't go into 3 so I put a zero on top .

    When it gets to 4 into 2(from 30-4x7), it doesn't go, so why don't I put a zero on top but instead put a zero beside the 2 to make it 20 ?


    thankyou



    roger
     
  2. jcsd
  3. Oct 24, 2004 #2

    dav2008

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  4. Oct 24, 2004 #3

    arildno

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    roger:
    Do you want to perform 3:4 or 4:3?
     
  5. Oct 24, 2004 #4

    DEAR ARILDNO,

    I AM TRYING TO DO 3 DIVIDED BY 4 LONG DIVISION

    BUT WHY DONT I PUT A ZERO ON TOP FOR 4 INTO 2 ?

    ROGER
     
  6. Oct 24, 2004 #5

    dav2008

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    Look at my link.

    You never put a 0 on top.

    What you do in the first step is put a decimal point on top.
     
  7. Oct 24, 2004 #6

    just looking at the link...

    when you do 7x4 =28

    and then 30 minus 28 = 2.

    from here

    4 doesnt go into 2 so why don't I put a zero on top ?

    This is what I want to know ....


    thanx


    roger
     
  8. Oct 25, 2004 #7

    arildno

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    Now, since to write down the long-division algoritm is a bit difficult (and besides, we do it differently in Norway from the US), I will show you the RATIONALE behind the long division technique instead; long division is simply a condensed version of what I'll present.

    1. What is meant by "division" in this case?
    Ordinarily, "division" is meant to be that process that rewrites a number, given as a FRACTION, into the equivalent DECIMAL REPRESENTATION of that number (which, as it happens, is a particular TYPE of fractional representation).
    2. Let's look at the number given by fraction 3/4

    We want to write 3/4 in its decimal representation, that is to find digits [tex]a_{i}[/tex] between 0 and 9, so that we have:
    [tex]\frac{3}{4}=0.a_{1}a_{2}a_{3}....[/tex]
    Where the notation [tex]0.a_{1}a_{2}a_{3}....[/tex] MEANS:
    [tex]0.a_{1}a_{2}a_{3}....\equiv\frac{a_{1}}{10}+\frac{a_{2}}{100}+\frac{a_{3}}{1000}++[/tex]

    3. Let's start!
    a) We note that 3<4, so our first step is to multiply 3/4 with an appropriate representation of the number "1":
    [tex]\frac{3}{4}=1*\frac{3}{4}=\frac{10}{10}*\frac{3}{4}=\frac{1}{10}*(\frac{30}{4})[/tex]
    Henceforth, we will work with the expression included in the parenthesis.
    b)
    We note that 30>4, and the greatest multiple of 4 which is less than 30, is 4*7=28.
    Hence, we write 30=4*7+2
    We therefore have the equality:
    [tex]\frac{30}{4}=\frac{4*7+2}{4}[/tex]
    c)We now use the fact that we can split up a sum in the numerator into a sum of fractions:
    [tex]\frac{4*7+2}{4}=\frac{4*7}{4}+\frac{2}{4}=7+\frac{2}{4}[/tex]
    The last step follows since 4 is a common factor in both the numerator and denominator in the first fraction.
    d) Hence we have shown:
    [tex]\frac{3}{4}=\frac{1}{10}*(7+\frac{2}{4})[/tex]
    This can be rewritten as:
    [tex]\frac{3}{4}=\frac{7}{10}+\frac{1}{10}(\frac{2}{4})=0.7+\frac{1}{10}(\frac{2}{4})[/tex]
    e) We will now work with the parenthesized 2/4.
    Since 2<4, we multiply 2/4 by an appropriate version of 1:
    [tex]\frac{2}{4}=1*\frac{2}{4}=\frac{10}{10}*\frac{2}{4}=\frac{1}{10}*(\frac{20}{4})[/tex]
    f) We note that 20=5*4, so we have:
    [tex]\frac{2}{4}=\frac{1}{10}*(\frac{5*4}{4})=\frac{1}{10}*(5)=\frac{5}{10}[/tex]
    g) We now look back at the equation in d):
    [tex]\frac{3}{4}=0.7+\frac{1}{10}(\frac{2}{4})[/tex]
    With the result from f), we have:
    [tex]\frac{3}{4}=0.7+\frac{1}{10}(\frac{5}{10})=0.7+\frac{5}{100}=0.7+0.05=0.75[/tex]

    And that's our result..
     
    Last edited: Oct 25, 2004
  9. Oct 25, 2004 #8

    HallsofIvy

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    I'm confused about your question "WHY DONT I PUT A ZERO ON TOP FOR 4 INTO 2 ?" because I certainly WOULD put a 0 on top!

    4 goes into 3 0 times so I would put a 0 before the decimal point and continue:

    __0.
    4) 3.0

    Now, 4 divides into 30 (ignore the decimal point now- we've already taken care of it) 7 times: 4*7= 28

    __0.7
    4) 3.00
    _28_
    20
    and now 4 divides into 20 5 times, evenly

    __0.75_
    4) 3.000
    _2 8__
    20
    20

    Of course, you don't HAVE to put the "0 on top" because 0, after all, means NOTHING! 0.75 is the same as .75 although I think you will find that "0.75" is preferred in "formal" writing.
     
  10. Oct 25, 2004 #9
    I'm confused about your question "WHY DONT I PUT A ZERO ON TOP FOR 4 INTO 2 ?" because I certainly WOULD put a 0 on top!

    4 goes into 3 0 times so I would put a 0 before the decimal point and continue:

    __0.
    4) 3.0

    Now, 4 divides into 30 (ignore the decimal point now- we've already taken care of it) 7 times: 4*7= 28

    __0.7
    4) 3.00
    _28_
    20
    and now 4 divides into 20 5 times, evenly
    this is where my concern was...
    I thought it was 4 divides into 2 NOT 20.
    So is that to say because the decimal point has been put down, it is really the calculation of 30 divided by 4 ?
    Because if it had been 2 instead of 20, my question was if 4 does not go into 2, then why do I not put a zero on top to indicate this .And then I would have brought down a zero to make it 20 and proceed from there......
    If I ever have to bring down a zero, where does it come from ?
    __0.75_
    4) 3.000
    _2 8__
    20
    20

    Of course, you don't HAVE to put the "0 on top" because 0, after all, means NOTHING! 0.75 is the same as .75 although I think you will find that "0.75" is preferred in "formal" writing
     
  11. Oct 26, 2004 #10

    HallsofIvy

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    "Because if it had been 2 instead of 20, my question was if 4 does not go into 2, then why do I not put a zero on top to indicate this "

    And my answer was you certainly can "put a zero on top to indicate this."

    You don't HAVE to since ".75" is commonly understood as "0.75" although, in my opinion, 0.75 is better.
     
  12. Oct 26, 2004 #11




    It still doesn't answer my query because if I had done it my way, I would have got an answer of 0.705

    This is wrong it should be 0.75 but I'm referring to the zero after the 7 not before the decimal point ?


    Please help me to understand this


    Roger
     
  13. Oct 26, 2004 #12
    Ok, I don't understand why you WANT to put the zero on the top?

    Lets walk through an easy example the way you want to do it and the correct way:

    116/4

    ___2
    4)116

    2*4=8

    11-8=3

    Now 3/4=0

    ___20
    4)116

    bring down the 6

    36/4=9

    ___209
    4)116


    Does that look like the correct answer? No. The reason you don't put the 0 on the top is that you don't redivide the remainder from one step to the next.

    Good luck.
     
  14. Oct 27, 2004 #13

    dav2008

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    Your question is like asking "why don't you add a zero when you divide 30/5 and get 6, not 60"

    You just don't. That's how it's done.
     
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