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How to multiply and divide without calculator ? :)

Discussion in 'Mathematics and Physics' started by ElectroNewby, Sep 6, 2010.

  1. ElectroNewby

    ElectroNewby Member

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    I feel so dumb, I used to know that stuff, but about 15 years ago lol.

    I'll put you in context.

    Let's say I need to multiply 12,7 with 4,5

    I need to divide -170 by 1,2

    and to calculate this one: 3,4 x (6,64 - 8,1215).

    It's kinda a pain in the rear.. I don't remember how to do that stuff (I think we never had to deal with decimals back when I learned how to do that stuff).

    minus 170 ? Seriously, what the hell without a calculator !

    If anyone remember the technic to resolve these, truly appreciated.

    I know I'm a bit annoying asking 10 000 questions but I'm in a big revision of stuff I haven't seen in a lot of years and the teacher presumes everybody come straight from highschool with hard maths.. :|

    This is very basic, yet algebra is a piece of cake to me compared to this kid's stuff.
     
  2. Pommie

    Pommie Well-Known Member Most Helpful Member

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    To do it in your head is a little tricky but on paper you should be able to do it.

    Take -170/1.2 - just do 170/12 - 14*12=168 remainder 2. 2 divided by 12 is a little tricky but 20/12 is 1.6666. Put it together and you get 14.1666. Do times 10 to get 141.666 and change the sign to get -141.666.

    Same with 12.7*4.5. Do 127*45 and move the decimal place 2 to the left.

    Mike.
     
    Last edited: Sep 6, 2010
  3. ElectroNewby

    ElectroNewby Member

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  4. dave

    Dave New Member

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  5. 3v0

    3v0 Coop Build Coordinator Forum Supporter

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    There is an great book called "Math For Dummies". It has the methods and tricks used to do math without calculators.

    EDIT: That may not be the right title. I will post it the next time I am up at school where the book is.
     
    Last edited: Sep 6, 2010
  6. ElectroNewby

    ElectroNewby Member

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    Ok thanks.

    I made it through except a simple substraction.... 6.64 - 8.1215

    I can't get this one to work
    I need to do it like this:

    6.6400
    -8.1215
    ________

    I'm screwed because 8 is greater than 6 and is below...

    EDIT: Nevermind... I just do 8 - 6 then report my minus sign.
     
    Last edited: Sep 6, 2010
  7. tamerl4ne

    tamerl4ne New Member

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    I haven't worked on decimals, but I've gotten faster at multiplying whole numbers in my head using an old trick. If I have to do, say, 17x12, I break it up mentally into two parts: 17x10 + 17x2. Much easier. And the same principle applies to something like 9x143. I do it as 10x143 - 143. Obviously the closer one of the numbers is to a nice round number you know well, like 10 or 25 or 100, the easier it is.
     
  8. MrAl

    MrAl Well-Known Member Most Helpful Member

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    Hi,

    One way to divide 170 by 1.2 for example is:

    You know 1.2 goes into 120 exactly 100 times, so write 100.
    Now 170-120 leaves 50.
    1.2 goes into 48 exactly 40 times so write 40.
    Now 50-48 leaves 2.
    2 divided by 1.2 would go similar:
    20/12: 12 goes into 12 exactly 1 time, so write 1
    Now 20-12 leaves 8.
    80/12: 12 goes into 72 exactly 6 times, so write 6
    80-72 leaves 8, so we repeat the 6 again so write 6,
    and since this is recurrent we get 66666666...etc.
    Now add all the results:
    100+40+1+0.6+0.06+0.006...etc
    and we get
    141.66666...a repeating decimal.

    The basic idea is to break the number down into known whole divisions, and do it in pieces, then add the results.

    The reason this works is based on the algebraic distributive law:
    If d=a+b+c
    then d/x=(a+b+c)/x=a/x+b/x+c/x.

    The rule for signs is easy:
    If + and + then +.
    If - and - then +.
    If - and +, or + and - then -.
    In other words, same signs means the result is positive, different signs means the result is negative.
     
    Last edited: Oct 31, 2010
  9. Roff

    Roff Well-Known Member

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    OMG! I'm almost 70 years old. They taught this stuff in grade school! I suppose that, as the sum of knowledge increases, something's gotta give.
    On the other hand, my wife says our grandkids are learning long division in grade school in Georgia.
     
  10. MrAl

    MrAl Well-Known Member Most Helpful Member

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    Hi again,


    There is also the "approximation by differentials" method which works pretty well to approximate some things that are otherwise very hard to solve. The idea is to approximate the derivative of the function as a straight line and that makes things simpler and this is very handy sometimes. The basic fomula looks like this:
    f(x+dx)=f(x)+f'(x)*dx
    where
    f(x) is the function we want to find a solution for, and
    f'(x) is the derivative of that function.

    For example, say we want to find the square root of 5.
    First, the derivative of sqrt(x) is 1/(2*sqrt(x)).
    [Note from here on the equals sign "=" will be used to represent 'approximately equal to' rather than 'equal to']
    Next, we form the differential and knowing the square root of 4 is 2 we make x equal to 4 and so the differential dx is 1:
    f(x+dx)=f(4+1)
    Knowing x=4 and dx=1 we can set up the equation now:
    f(x+dx)=f(x)+f'(x)*dx
    and substituting:
    f(4+1)=f(4)+f'(4)*1
    or
    f(4+1)=2+1/4*1
    or
    f(4+1)=2.25
    so
    f(5)=2.25

    so the square root of 5 is approximately equal to 2.25

    We can also repeat the process by squaring 2.25 and using that as the next approximation. In this way, we can approximate to any degree of accuracy.
     
    Last edited: Nov 1, 2010
  11. tytower

    tytower Banned

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    There are a few tricks also worth studying and learning. You have to find them or u won´t remember them.

    Here´s one to start however

    Anything multipied by 11 write it down, then under it write it again ,but 1 column over, then add both lines

    11X 263 =........263
    ...................... 263..
    .......................2893

    It works backwards too if u know it goes into the number evenly
    Handy for GST in Aus where GST is 1/11th of final price
     
    Last edited: Nov 3, 2010
  12. Warlord_1011

    Warlord_1011 New Member

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    Id convert the decimals into fractions and then when a denomonator (the bottom number of a fraction) is a fraction it is the same as swapping it around and multiplying by the numerator for example

    Z/(X/Y) = Z*Y/X

    1/0.25 = 1/(1/4) = 1*(4/1), so the answer to 170 divided by 1.2 is:

    170/1.2 = 170/(6/5) = 170*5/6 = 850/6 = 425/3 then you can calculate that to an exact value around 141
     

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