find the quotient and remainder when 11,109,999,999,997 is divided by 1111
I came up with q=1,111 r=10
Is this right?
Nope!
Quotient will be 999999999 and remainder will be 1108
first 4 digits are 1110 so if you take first digit of quotient as 1 then you will have to subtract 1111 from 1108 which is negative so instead of taking first 4 digits take first five digits that is 11109.
I think it's easier if you consider that the dividend is *almost* 11,110,000,000,000. If you divide this by 1111 you get 10,000,000,000. since 11,109,999,999,997 is only three less than 11,110,000,000,000 then it is clear that 1,111 goes into the first number one less time than the second...which gives nikhil's result. And it should be clear that the remainder will be 1108, because if your number were 3 more it would be divisible by 1,111.
$\displaystyle \color{white}.\quad.$$\displaystyle 11\,109\,999\,999\,997$
$\displaystyle =\ 11\,110\,000\,000\,000-3$
$\displaystyle =\ 11\,110\,000\,000\,000-1111+1108$
$\displaystyle =\ 1111\times(10\,000\,000\,000-1)+1108$
$\displaystyle =\ 1111\times\underbrace{9\,999\,999\,999}_{\textrm{q uotient}}\,+\,\underbrace{1108}_{\textrm{remainder }}$