Question

A mixed fraction is given as $1\dfrac{3}{7}$. Convert this mixed fraction into improper fraction.

Answer 1

Hint: In this question a mixed fraction is given and we have to write it in the form of improper fraction. First of all write the given mixed fraction in the terms of addition of two numbers 1 and $\dfrac{3}{7}$ and then add these two numbers.

Complete step-by-step answer:

In the question, it is given that we have to convert the given mixed fraction into improper fraction.
First of all we will see what is a mixed fraction and how it is formed.
The mixed fraction is in the form of ${\text{a}}\dfrac{{\text{p}}}{{\text{q}}}$ .
Where a, p and q are integers and ${\text{q}} \ne {\text{0,1}}$ and ${\text{a}} \geqslant {\text{1}}$ .
It can be written in the form of addition as follow:
${\text{a}}\dfrac{{\text{p}}}{{\text{q}}} = a + \dfrac{{\text{p}}}{q}$
On solving the above addition we will get an improper fraction because ${\text{a}} \geqslant {\text{1}}$.
So the given mixed fraction can be written as:
$1\dfrac{3}{7} = 1 + \dfrac{3}{7}$.
The above two numbers are integers and a proper fraction respectively. To add these numbers, we will first take the LCM of the denominator and then divide the LCM by denominator and multiply the result by numerator. In this way we get:
$1 + \dfrac{3}{7} = \dfrac{{7 + 3}}{7} = \dfrac{{10}}{7}$.

$\because $ In $\dfrac{{10}}{7}$ , the numerator is greater than the denominator. So it is an improper fraction.
Therefore the mixed fraction $1\dfrac{3}{7}$ is converted into an improper fraction $\dfrac{{10}}{7}$.

Note: In this type of question you should remember the definition of proper fraction, improper fraction and mixed fraction. You can also solve this question by multiplying the denominator i.e.7 by 1 and then add the numerator to the product to get the answer as an improper fraction. If a number is an improper fraction then it will be always greater than 1.