Answer

Verified

373.2k+ 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

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Name 10 Living and Non living things class 9 biology CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

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

Write a letter to the principal requesting him to grant class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail