Question

How do you write mixed fractions into improper fractions?

Answer 1

We first try to explain the mixed fraction and the representation in improper fraction. We use variables to express the condition between those representations. Then we apply long division to express the improper fraction in mixed fraction. We take an example to understand the concept better.

Complete step by step solution:
Improper fractions are those fractions who have greater value in numerator than the denominator.
We need to convert the mixed fraction which is representation in the form sum of an integer and a proper fraction. We express the process in the form of variables.
Let the mixed fraction be $x\dfrac{c}{b}$. The condition is $c<b$. $x\dfrac{c}{b}$ can be expressed as $x+\dfrac{c}{b}$. Now we express it in the form of improper fraction. Let’s assume the improper fraction is $\dfrac{a}{b}$ where $a>b$.
Then the equational condition will be $\dfrac{a}{b}=x+\dfrac{c}{b}$.
The solution of the equation $x+\dfrac{c}{b}=\dfrac{bx+c}{b}$.
This means $\dfrac{a}{b}=\dfrac{bx+c}{b}$. Therefore, the final condition for the fraction will be $a=bx+c$.
Now we solve a mixed fraction $5\dfrac{5}{6}$. So, $5\dfrac{5}{6}=5+\dfrac{5}{6}$
The integer is 5 and the proper fraction is $\dfrac{5}{6}$.
We express it as a multiplication form. We use $a=bx+c$.
So, $a=5\times 6+5=35$
Therefore, the improper fraction is $\dfrac{35}{6}$.
The simplified representation of the fraction $5\dfrac{5}{6}$ is $\dfrac{35}{6}$.

Note: We need to remember that the denominator in both cases of improper fraction and the mixed fraction will be the same. The only change happens in the numerator. The relation being the equational representation of $a=bx+c$.