Exploring Division

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    • #28993
      Pasyanthi
      Keymaster

      Exploring Division

      This thread has been created to complement the “Exploring Multiplication” thread and to discuss the area of division.

      To start off, suppose you want to find 847 divided by 236 to several decimal places.

      You could have 2 as a divisor and 36 on the flag, but that would not work well (as 2 is too small for a good divisor).
      You could have 23 as a divisor and 6 on the flag, but then you are dividing by 23 at each step.

      What do you suggest?

      And if you want to pose your own division question for the rest of us to tackle please do so in this thread.
      See if you can find a particulary difficult one.

      Here are four division methods covered in the course:

      1.                 Division by 9, 8, 11, x+1 etc., Lesson 18

      2.                 Reversing multiplication, numerical and algebraic, Lesson 13

      3.                 Straight division (general method), Lessons 25, 26

      4.                 Recurring decimals, Lessons 31, 32

    • #31770
      Anupama Cherukuri
      Participant

      Can we halve 236 to 118 and divide 847 by 118 in the straight division method.

      847  divided by 118 in straight division method I got 7.18 and If I halve 7.18 the answer is 3.59

       

      Thanks

       

       

       

      • #31901
        KennethWilliams
        Keymaster

        Yes, that’s an excellent method Anupama.

    • #32019
      Savita P Kulkarni
      Participant

      Hi,

      Anupama, you have suggested an easy way.

      i tried reverse multiplication method,

      ?? *236=847 (by vertically and crosswise ), could not solve it as this is a 2 digit by 3 digit no multiplication.

      Then i went on to solve it by using bar no. 24(4) and 2 as a divisor and 4(4) raised on the flag – it was a little bit of thinking to not get a negative  but i got the answer as 3.59.

      Mr. Ken, for such complex division I think I would have started with the st. division as it is an general method, but as you said 2 is too small to be a good divisor and 36 as a flag was difficult to work with. How do we proceed?

      Division by 8, 9, 11 does not seem useful. Do we try x+1?

      Thank you,

      • #32053
        KennethWilliams
        Keymaster

        Hi Savita,

        It’s good you are exploring like this. It is like in ordinary life, we are prepared to make the adjustments we need to make the problem easy or manageable.

        Anupama’s method for this particular division is probably as good as it gets. But for the divison by 118 you could use 12 as divisor witj (2) on the flag.

        Or, you could halve both 847 and 236 (saves the halving at the end).
        Or you could double 236 and work with a divisor of 5.

        The reverse multiplication method will work too.

    • #32986
      Preeti Pathak
      Participant

      Hi !!!
      can we do this way?
      if we write 847/236 = 847/59 * 1/4
      then 59 can be written as 6(1).
      847/6(1)

      taking 6 as divisor and (1) as bar digit, got answer =14.35
      and then halving it twice,14.35/2=7.175, 7.175/2=3.5875
      847/236=3.588

      • #33017
        KennethWilliams
        Keymaster

        Excellent Preeti. That is a really good way to do the division.

        These little tweaks are simple to do and make the problem much easier.

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