Question

How do you write $ \dfrac{22}{3} $ as a mixed fraction?

Answer 1

Hint: In this question, we need to write a given fraction into a mixed fraction. The fraction is given in improper fraction form. For converting, we will first divide the numerator of the fraction with the denominator. The integral part of the answer (quotient) will be the whole number part of the fraction. The remainder will be the numerator fraction part and the denominator will remain the same.

Complete step by step answer:
Here we are given an improper fraction as $ \dfrac{22}{3} $ .
We need to change it to a mixed fraction.
Let us first understand the meaning and some examples of mixed fractions. A mixed fraction is a form of the fraction which is defined as the ones having a fraction and a whole number. For example, $ 3\dfrac{1}{4} $ is a mixed fraction in which 3 is the whole number in part and $ \dfrac{1}{4} $ is the fraction part. A mixed fraction can also be stated as $ 3+\dfrac{1}{4} $ .

$\Rightarrow$ Now let us convert the given improper fraction to mixed fraction. For this we first need to divide the numerator by the denominator. Here we need to divide 22 by 3 we get,
 $ 3\overset{7}{\overline{\left){\begin{align}
  & 22 \\
 & 21 \\
 & \overline{01} \\
\end{align}}\right.}} $
We have obtained the quotient as 7 and the remainder as 1.
For writing the mixed fraction, the quotient is written as the whole number part and the remainder is written as the numerator of the fractional part. The denominator of the fraction part is the same as the original denominator or we can say the denominator of the fractional part is the divisor of the division performed. So our mixed fraction looks like this, $ 7\dfrac{1}{3} $ . This is the required answer.

Note:
Students should not get confused between quotient and remainder. They can check their answers in following way, if mixed fraction is of form $ a\dfrac{b}{c} $ its improper fraction is given by $ \dfrac{\left( a\times c \right)+b}{c} $ . So, here for $ 7\dfrac{1}{3} $ we have \[\dfrac{\left( 7\times 3 \right)+1}{3}=\dfrac{21+1}{3}=\dfrac{22}{3}\] which is the original answer. Hence our answer is correct. Shortcut way to remember the order of writing a mixed fraction is $ Q\dfrac{R}{D} $ where Q is quotient, R is remainder and D is divisor.