# math: why do we divide the way we do?

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• 11-04-2005
jrahhali
math: why do we divide the way we do?
Code:

```    2.8   ___ 5| 14   -10   ---     4 0```
i'm a bit confused behind the logic of this "long hand" way to division.

ok, so
5 goes into 14 2 times, so you write a 2. you then subtract the amount of times 5 can go into 14 from 14, and you get 4. Up to this point, i understand it.

why, now, do you bring down a 0, and see how many times 5 can go into 40? why does this give you your fractional part, logically?
• 11-04-2005
Govtcheez
Technically it's how many times it goes into 4.0, but it's a lot easier to look at it as 40 instead. The decimal point does actually come down, but we never show it because it's a lot easier to learn that way.
• 11-04-2005
VirtualAce
A whole number is not just the integer part that you see.

4/100 = 25

But it's 4.00... /100.00...

The zeroes are not made up, they are really there since there is 0 amount of tenths, hundreths, etc. That's why you bring the zero down because it is really there and it allows you to continue the division.
• 11-05-2005
Rashakil Fol
The algorithm uses this relationship:

For all values of k, x/y = k/y + (x-k)/y

For example:
Code:

```To divide 84732/7, let: 84732/7 = 10000 * (8/7)    + 4732/7  (We lop off all but the last         = 10000 * (1 + 1/7) + 4732/7  four digits.)         = 10000 + 10000/7  + 4732/7         = 10000 + 14732/7            (At this point, we write down '1'.) 14732/7 =  1000 * (14/7)    + 732/7  (We lop off all but the last         =  1000 * (2 + 0/7) + 732/7    three digits.)         =  2000 + 0/7      + 732/7         =  2000 + 732/7              (At this point, we write down '2'.)   732/7 =  100 * (7/7)    + 32/7    (We lop off all but the last         =  100 * (1 + 0/7) + 32/7    two digits.)         =  100 + 0/7      + 32/7         =  100 + 32/7                (At this point, we write down '1'.)   32/7 =    10 * (3/7)    + 2/7    (We lop off all but the last         =    10 * (0 + 3/7) + 2/7      one digit.)         =    0 + 30/7      + 2/7         =    0 + 32/7                (At this point, we write down '0'.)   32/7 =    1 * (32/7)    + 0/7    (We lop off all the digits.)         =    1 * (4 + 4/7) + 0/7         =    4 + 4/7      + 0/7         =    4 + 4/7                (At this point, we write down '1'.)     4/7 =  0.1 * (40/7)    + 0/7    (We 'lop off' past the decimal         =  0.1 * (5 + 5/7) + 0/7      place.)         =  0.5 + 0.5/7    + 0/7         =  0.5 + 0.5/7              (We write a decimal point and a                                       '5'.)   0.5/7 =  0.01 * (50/7)    + 0/7         =  0.01 * (7 + 1/7) + 0/7         =  0.07 + 0.01/7    + 0/7         =  0.07 + 0.01/7              (We write down a '7'.) And so on and so forth.```
Substituting expressions back up, we get the answer:
Code:

```10000 + 2000 + 100 + 00 + 4 + 0.5 + 0.7 + 0.01/7 = 12104.57 + 0.01/7```
• 11-05-2005
VirtualAce
Ok.

Our numbers are base 10. So:

12500 is

1 * (10^4)+
2 * (10^3)+
5* (10^2)+
0 *(10^1)+
0 *(10^0)

for decimals

.01 is
0 * (10^-1)+
1 * (10^-2)

I'm not sure where the other stuff from above came from, but this is why we drop zeros. If the value was not zero, you would drop that value.
• 11-05-2005
white
did anyone knows that there is a similar way of finding the square root of any number?
http://www.nist.gov/dads/HTML/squareRoot.html
• 11-05-2005
jrahhali
>>Technically it's how many times it goes into 4.0, but it's a lot easier to look at it as 40 instead.

ok. since there are 5 8's in 40, then there should 5 0.8's in 4.
• 11-05-2005
gcn_zelda
Quote:

Originally Posted by white
did anyone knows that there is a similar way of finding the square root of any number?
http://www.nist.gov/dads/HTML/squareRoot.html

I think I'll stick to local linear approximation.