View Full Version : math: why do we divide the way we do?

jrahhali

11-04-2005, 02:57 PM

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?

Govtcheez

11-04-2005, 04:00 PM

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.

VirtualAce

11-04-2005, 11:55 PM

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.

Rashakil Fol

11-05-2005, 12:37 AM

The algorithm uses this relationship:

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

For example:

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:

10000 + 2000 + 100 + 00 + 4 + 0.5 + 0.7 + 0.01/7

= 12104.57 + 0.01/7

VirtualAce

11-05-2005, 12:59 AM

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.

white

11-05-2005, 02:00 AM

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

jrahhali

11-05-2005, 11:00 AM

>>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.

gcn_zelda

11-05-2005, 05:15 PM

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.

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