Question

Mixed fraction for \[\dfrac{{39}}{{12}}\] is
A.\[3\dfrac{1}{{12}}\]
B.\[3\dfrac{2}{{12}}\]
C.\[3\dfrac{3}{{12}}\]
D.\[2\dfrac{{14}}{{12}}\]

Answer 1

Hint: We will divide the numerator of the fraction by the denominator of the fraction. We will find the quotient and the remainder (if there is any). We will write the quotient on the left side as a whole number. On the right side, we will write a fraction whose numerator will be the remainder that we have obtained and the denominator will be the denominator of the original fraction.

Formula used: We will use the formula, \[\dfrac{{\rm{N}}}{{\rm{D}}} = {\rm{Q}}\dfrac{{\rm{R}}}{{\rm{D}}}\] where N is the numerator of the original fraction, D is the denominator of the original fraction, Q is the quotient obtained on dividing N by D and R is the remainder obtained on dividing N by D.

Complete step-by-step answer:
Here we are provided with a fraction which we need to convert into mixed fraction. For this we need to understand different types of fractions. These are:
Proper Fractions: The fractions in which the denominator is greater than the numerator are called proper fractions.
Improper Fractions: The fractions in which the denominator is smaller than the numerator are called improper fractions.
Mixed Fractions: They are the fractions that are written as a mixture of whole numbers and proper fractions. Usually, improper fractions are converted into mixed fractions.
We will divide the numerator by the denominator:
\[\begin{array}{*{20}{c}}{12\mathop{\left){\vphantom{1{39}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{39}}}}
\limits^{\displaystyle\,\,\, 3}}\\\begin{array}{l}\underline { - {\rm{ }}36} \\{\rm{ }}3\end{array}\end{array}\]
We know that \[12 \times 3 = 36\] and that 39 is 3 more than 36.
We have obtained the quotient as 3 and remainder as 3 as well.
We will substitute 3 for Q, 3 for R, 39 for N and 12 for D in the formula \[\dfrac{{\rm{N}}}{{\rm{D}}} = {\rm{Q}}\dfrac{{\rm{R}}}{{\rm{D}}}\]:
\[\dfrac{{39}}{{12}} = 3\dfrac{3}{{12}}\]
\[\therefore\] Option C is the correct option.

Note: We should not be alarmed if we see \[3\dfrac{1}{4}\] as an option. \[3\dfrac{3}{{12}}\] can also be expressed as \[3\dfrac{1}{4}\]. The numerator and denominator have 3 as the common factor. We know that the unique representation of a fraction is the one in which the numerator and denominator don’t have any common factor except 1. We can represent \[\dfrac{3}{{12}}\] uniquely in the following manner:
\[\dfrac{3}{{12}} = \dfrac{3}{{4 \times 3}} = \dfrac{1}{4}\]