Question

What is \[336 \div 12\]?

Answer 1

Hint: Division: Consider \[\dfrac{a}{b}\] where \[a\] is called as a dividend and \[b\] is called as a divisor. \[\dfrac{a}{b} = q\dfrac{r}{b}\], where \[0 \leqslant r < b;\,\,\,q \in \mathbb{Z}\], \[q\] is a quotient, \[r\] the remainder and the form is mixed fraction.
Every term in the dividend is called a numerator and every term in the divisor is called the denominator.

Complete step-by-step solution:
From the given problem we need to solve the \[336 \div 12\]
Clearly, by using the long division method or by cancelling it with term by terms in the both numerator and denominator at a time we get,
\[\dfrac{{336}}{{12}} = \dfrac{{168}}{6}\]
Cancelling the above expression by \[2\] in the both numerator and denominator we get,
\[\dfrac{{168}}{6} = \dfrac{{84}}{3}\]
Again, by cancelling the above equation by \[3\] in the both numerator and denominator we get,
\[\dfrac{{84}}{3} = 28\]
Therefore, the quotient and the remainder are\[q = 28;\,\,\,r = 0\].
Hence, the required answer \[336 \div 12 = 28\].

Note: It is important to note that \[\dfrac{1}{0} = {\text{undefined}}\] and \[\dfrac{0}{1} = 0\], also we should avoid \[\dfrac{0}{0}\] which is an indeterminate form. As we cannot handle the problems in which we have a problem in which the terms who’s both the numerator and denominator is zero. Because if the denominator gets larger and larger the fraction becomes smaller and smaller, and the value becomes zero. And also if the denominator gets smaller and smaller, the fraction becomes larger and larger and thus, the fractional value gives undefined and hence it is denoted by infinity and has the symbol \[\infty \]. And when anyone of the numerator or denominator becomes larger and larger or smaller and smaller then fraction becomes meaningless or doubtful.