Question

Divide (-117) by 9.

Answer 1

Hint: An integer (from the Latin integer meaning "whole” is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75 is not an integer.

Complete step by step answer:
So we know that 117 is completely divisible by 9 because if we add all the digits of 117 we will get \[1 + 1 + 7 = 9\] and 9 is divisible by 9 so we will first divide 117 by 9 and then as it is completely divisible so we won't have any remainder so just after the whole division we will have to put a negative sign in front of the quotient we will get
\[9\mathop{\left){\vphantom{1\begin{array}{l}
117\\
 - 9\\
\begin{array}{*{20}{c}}
{\_\_\_}\\
{27}\\
\begin{array}{l}
 - 27\\
\_\_\_\_
\end{array}\\
\begin{array}{l}
0\\
\_\_\_\_
\end{array}
\end{array}
\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}
117\\
 - 9\\
\begin{array}{*{20}{c}}
{\_\_\_}\\
{27}\\
\begin{array}{l}
 - 27\\
\_\_\_\_
\end{array}\\
\begin{array}{l}
0\\
\_\_\_\_
\end{array}
\end{array}
\end{array}}}}
\limits^{\displaystyle \,\,\, {13}}\]

Hence we are getting the quotient as 13 if we take 117 as positive so if we put a negative sign in front of it then we will get -13 as quotient here.

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.