parallel_chase wrote:Here is a definition to help you understand remainders better.
"when the result of the division of two integers cannot be expressed with an integer quotient, the remainder is the amount "left over."
The quotient can have decimal values.
if you divide 1 by 3, the quotient will be .333.... and this will always leave a remainder of 1.
Similarly if you divide 10 by 6, the quotient can be 1.6666 and this will always leave a remainder of 4.
Hope this helps.
When we talk about quotients in the context of quotients and remainders, we almost always mean the 'integral quotient'. An integral quotient is never a decimal, always an integer. When you divide n by d, you can always find (assuming n and d are positive integers), unique integers q and r so that:
n = qd + r, where 0 <= r < d
q is called the integral quotient, or more usually, just the 'quotient';
r is called the 'remainder'.
When you divide 10 by 6, the quotient is 1 and the remainder is 4, because
10 = 1*6 + 4
When you divide 1 by 3, the quotient is 0 and the remainder is 1, because
1 = 0*3 + 1
To answer beeparoo's question, M+N can equal ten because quotients can be equal to zero (in your notation, one of x or y could be zero, and the other could be one).
