Question

Find the quotient and remainder of \[ - 50 \div 7\] .

Answer 1

Hint: Divide it normally you don't need to make the divisor negative. Just after solving all the things, put a negative sign in front of the quotient.
Complete Step by Step solution:
 So Divide it normally and we will get it as
$\begin{array}{*{20}{c}}
{7)}&{50}&{(7}&{}\\
{}&{ - 49}&{}&{}\\
{}&{\_\_\_\_\_\_\_\_\_}&{}&{}\\
{}&1&{}&{}
\end{array}$
Now in the positive terms we are getting the quotient as 7 and remainder as 1
But in the question it is given as \[ - 50 \div 7\]
Therefore we will put a negative sign in front of the quotient So now the quotient and remainder becomes -7 and 1 respectively.
A remainder cannot be negative because that simply means that we are multiplying greater factors in quotients which is effectively becoming greater than the dividend itself and that's against the rule of dividing.

Note: It must be noted that a quotient can be in negative but a remainder cannot be in negative for a regular division despite the fact that the divisor or dividend are in positive or negative the remainder is always in positive. If we see that a remainder is negative that means we should subtract that many from the divisor. For example \[167 \equiv - 2(\bmod 13)\] where -2 is the remainder and 13 is the divisor is simply equivalent to \[167 \equiv 11(\bmod 13)\] which means remainder was never zero its just a form of writing it to solve further.