Answer

Verified

408.3k+ views

**Hint:**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 $\dfrac{35}{6}$.

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 $a=bx+c$.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE