Question

How do you write $6{\displaystyle \frac{1}{2}}$ an improper fraction?

Answer 1

Hint:
Whenever we have mixed fraction problems, we need to remember one thing that the mixed fraction of the form $a{\displaystyle \frac{b}{c}}$ can be written as ${\displaystyle \frac{ac+b}{c}}$. The fraction of the form ${\displaystyle \frac{ac+b}{c}}$ is nothing but the improper fraction. So by using the general form of improper fraction that is ${\displaystyle \frac{ac+b}{c}}$ we can arrive at the required answer.

Complete step by step solution:
In the given question they have given mixed fraction, and asked us to convert mixed fraction to an improper fraction.
Whenever we have a numerator value in the fraction that is greater than the denominator value then we call such a fraction an improper fraction. If the numerator value is less than the denominator value then that fraction is called proper fraction. For example: ${\displaystyle \frac{5}{2}},{\displaystyle \frac{20}{3}}$ are examples of improper fraction while ${\displaystyle \frac{6}{12}},{\displaystyle \frac{2}{5}}$ are examples of proper fraction as the numerator is less than the denominator.
So here we have given the mixed fraction which comprises of the integer and the proper fraction in the form of $a{\displaystyle \frac{b}{c}}$ where $a$ is the integer and ${\displaystyle \frac{b}{c}}$ is the proper fraction.
So here we need to remember one thing that whenever we have the mixed fraction of the form $a{\displaystyle \frac{b}{c}}$ we can convert it into an improper fraction by using the general form of an improper fraction given by: ${\displaystyle \frac{ac+b}{c}}$.
Now compare $a{\displaystyle \frac{b}{c}}$ with the mixed fraction we have given in the question that is $6{\displaystyle \frac{1}{2}}$, therefore we get $a=6,b=1$ and $c=2$ .
We know that the improper fraction can be written as ${\displaystyle \frac{ac+b}{c}}$ from the mixed fraction of the form $a{\displaystyle \frac{b}{c}}$.
Now, substitute the value of $a,b,c$ in the improper fraction ${\displaystyle \frac{ac+b}{c}}$ , we get
Improper fraction $={\displaystyle \frac{ac+b}{c}}={\displaystyle \frac{(6\times 2)+1}{2}}$
On simplifying the above expression, we get
Improper fraction $={\displaystyle \frac{12+1}{2}}$

Therefore, Improper fraction $={\displaystyle \frac{13}{2}}$.

Note:
Whenever we have this type of conversion problem, you have to remember the definition of proper fraction, improper fraction, and the mixed fraction in order to differentiate between these types of fractions. And when they ask to convert from mixed fraction to improper fraction one important thing you need to remember is we can write the mixed fraction of the form $a{\displaystyle \frac{b}{c}}$ as ${\displaystyle \frac{ac+b}{c}}$ which is an improper fraction form.