Question

What is $\dfrac{11}{3}$ in a mixed number?

Answer 1

Hint: Considering 11 as the dividend and 3 as the divisor, we will divide 11 by 3 to get the required quotient (a) and remainder (b). Now, we will write this improper fraction in the form $a\dfrac{b}{c}$ to get the required mixed fraction. Here (c) is the divisor 3.

Complete step by step answer:
Here we have been provided the improper fraction $\dfrac{11}{3}$ and we are asked to convert it into the mixed fraction. But first let us see the meaning of an improper fraction, mixed fraction and the general form of a mixed fraction.
Now, an improper fraction is a type of fraction whose numerator is greater than its denominator. For example: $\dfrac{99}{5}$. If the numerator is larger than the denominator then we use the term proper fraction. For example: $\dfrac{5}{9}$.
Now, a mixed fraction is of the form $a\dfrac{b}{c}$ where (a) is quotient, (b) is remainder and (c) is the divisor. Generally we only convert an improper fraction into mixed fraction. To do so, we divide the numerator with the denominator and find the quotient and remainder and substitute these into the general form $a\dfrac{b}{c}$ to get the answer.
Let us come to the question. To convert $\dfrac{11}{3}$ into a mixed fraction we have to divide 11 by 3. So, dividing 11 by 3 we have quotient (a) = 3, remainder (b) = 2 and divisor (c) = 3. Therefore, substituting these values in the general form we get,
$\therefore \dfrac{11}{3}=3\dfrac{2}{3}$

Hence, our answer is $3\dfrac{2}{3}$.

Note: You must know the conversion relation of an improper fraction into a mixed fraction otherwise it will be difficult to solve the above question. Note that the mixed fraction $a\dfrac{b}{c}$ is read as ‘a whole b divided by c’ and mathematically it is equivalent to the sum $a+\dfrac{b}{c}$. The reason that a proper fraction is not converted into a mixed fraction is that, here the quotient will be less than 1 so it will be inconvenient to transform it.