Question

Convert the following improper fraction into fixed fraction $\dfrac{7}{3}$.

Answer 1

Hint: We will use the concept of division here. In the division method we simply divide the numerator by the denominator.

Complete step-by-step solution -
According to the question we are supposed to convert the fraction $\dfrac{7}{3}$ into a mixed fraction. First we will discuss about the term mixed fraction. A mixed fraction is a type of number which includes any number from the integer family combined with a fraction part. For example $2\dfrac{1}{3}$ is called a mixed fraction. If we notice then we can find out that this mixed fraction has the combination of an integer number which is 2 and a fraction as $\dfrac{1}{3}$. To convert any fraction into a mixed fraction we will apply the concept of division. For that let us consider a fraction of the form $\dfrac{a}{b}$. Here, ‘a’ is the numerator and ‘b’ is called the denominator. Now, we will divide a by b. Then, we have ‘a’ as a dividend and ‘b’ will be known as a divisor. The division takes part as follows,
$a\overset{c}{\overline{\left){\begin{align}
  & \,\,\,b \\
 & \underline{\pm b} \\
 & \,d \\
\end{align}}\right.}}$
Here, we also see that ‘c’ is working here as a quotient and ‘d’ is known as a remainder. So, the fraction $\dfrac{a}{b}$ can be written as $c\dfrac{d}{a}$.
Now, we will apply the same procedure to the fraction $\dfrac{7}{3}$.We will divide the number 7 by 3. Therefore, we have
$3\overset{2}{\overline{\left){\begin{align}
  & \,\,\,7 \\
 & \underline{\pm 6} \\
 & \,\,\,1 \\
\end{align}}\right.}}$
So, we now have 7 as a dividend, 3 as a divisor, 2 as a quotient and 1 as a remainder. Therefore, the required mixed fraction can be formed as $2\dfrac{1}{3}$.
Hence, the mixed fraction of the fraction $\dfrac{7}{3}$ is $2\dfrac{1}{3}$.

Note: The diving part may be found out as an easy part but the important part here is placing the numbers into a mixed fraction. For that we also need to understand about the terms dividend, divisor, quotient and remainder. And these have been explained in the solution.