Question

How can you write \[42/7\] as a mixed fraction?

Answer 1

Hint: For this, we need to first divide the numerator by the denominator. Then we need to find the quotient and remainder. Then, we just make the given representation of the divisor \[\left( d \right)\], quotient \[\left( q \right)\] and remainder \[\left( r \right)\] – \[q\dfrac{r}{d}\], and this is the required mixed fraction.

Complete step by step answer:
The given improper fraction is \[f = \dfrac{{42}}{7}\].
First, we divide the fraction. Then we need to find the quotient and remainder. Then, we just make the given representation of the divisor \[\left( d \right)\], quotient \[\left( q \right)\] and remainder \[\left( r \right)\] – \[q\dfrac{r}{d}\], and this is the required mixed fraction.
\[7\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ }}42\\\dfrac{{ - 42}}{0}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ }}42\\\dfrac{{ - 42}}{0}\end{array}}}}
\limits^{\displaystyle\,\,\, 6}\].

So, this number is perfectly divisible, hence, in the conventional form, it is written as a natural number, but, if we have to write it as a mixed fraction, we get it as,
\[\dfrac{{42}}{7} = 6\dfrac{0}{7}\]
Hence, \[\dfrac{{80}}{5} = 16 = 16\dfrac{0}{5}\].

Additional Information:
The given mixed fraction can also be represented as:
\[f = 6 + \dfrac{0}{7}\]
Hence, if \[f = a\dfrac{b}{c}\], then it is same and can be represented as
\[f = a + \dfrac{b}{c}\]

Note: The mixed fractions are represented in two ways in which both are equal: \[a\dfrac{b}{c}\] or \[a + \dfrac{b}{c}\]. Both of these mean the same thing, just a little different way to show it.