The math help thread

A friend of mine got this question on his assignment, basically x can be any digit. Somebody in our grade (9) got the answer but I don't know how. Could somebody explain this?

......___.xxx
xxx/xxx.
.....xxx.x
....-xxx.x
........0.xxx
.........-.xxx
.........0.000

(dots on the left are place-holders)

Work backwards =P It's a logic puzzle basically

Code:

___.xxx
xxx/xxx.
    xxx.x
   -[U]xxx.x[/U]
      0.xxx
      -[U].xxx[/U]
       .000

abc is a multiple of ijk. efg.h is an even bigger multiple of ijk.

Code:

___.xxx
ijk/xxx.
    xxx.0
   -[U]efg.h[/U]
      0.abc
      -[U].abc[/U]
       .000

mno is smaller than ijk, otherwise there's no need to tack on an extra decimal digit BEFORE subtracting once.

Code:

___.x0x
ijk/mno.
    mno.0
   -[U]efg.h[/U]
      0.abc
      -[U].abc[/U]
       .000

Notice how bc is also tacked on at the end in abc. Those can only be 0's. Also, mn = ef since mn-ef = 0.

Code:

___.x0x
ijk/mno.
    mno.0
   -[U]mng.h[/U]
      0.a00
      -[U].a00[/U]
       .000

g is 1 less than o. Something like 1230 - 1227 = 3 or something (in this case, g = 2, o = 3).

Now, we know that h =/= 0, since 10 - h = a, and that a =/= 0 or else the division would have ended already. We know that ijk multiplied by some number = a00. We also know that ijk multiplied by a bigger number = mng.h. Now we ask, what number t below 10 can we use to multiply jk so that it equals 100 or 200, etc? k cannot be 0 due to h being non-zero. Also, we must make sure that ijk multiplied by t doesn't go over 1000. Here are the possibilities:

Code:

k = 8, 6, 5, 4, 2
t = 5, 5, 2, 5, 5
          4
          6
          8

jk = 25
t  = 4

At this point, we can probably guess the numbers.

Code:

___.904
125/113.
    113.0
   -[U]112.5[/U]
      0.500
      -[U].500[/U]
       .000

Sorry if it was confusing >.<