Question

How do you write $11\dfrac{3}{4}$ as an improper fraction?

Answer 1

Hint: Given the mixed number and we have to write it in the form of improper fraction. In improper fractions the number written at the numerator is always larger than the number at the denominator. To convert the mixed fraction to improper fraction first, multiply the denominator of the fraction by the whole number. Then, add the resultant value to the numerator of the fraction and write it at the top of the denominator.

Complete step-by-step solution:
First, we will multiply the whole number $11$ by the denominator of the fraction $4$.
$ \Rightarrow 11 \times 4 = 44$
Now, we will add the result to the numerator of the fraction that is $3$.
$ \Rightarrow 44 + 3 = 47$
Now write the result at the top of the denominator of the fraction.
$ \Rightarrow \dfrac{{47}}{4}$

Hence the improper fraction of the mixed number is $\dfrac{{47}}{4}$

Additional Information: An improper fraction is the type of fraction in which the numerator is greater than or equal to the denominator in the expression. A mixed number is written as a whole number with a proper fraction.

Note: In such types of questions students mainly get confused in applying the formula. As they don't know which formula they have to apply. So when the number in the form of mixed fraction is given, then the value of the denominator is first multiplied with the whole number and then added to the numerator.
Alternate method:
We will write the expression $11\dfrac{3}{4}$ as the sum of the whole number and proper fraction.
$ \Rightarrow 11 + \dfrac{3}{4}$
$ \Rightarrow 1 \times 11 + \dfrac{3}{4}$
Now, we will write the number $1$ as a fraction with denominator$4$.
$ \Rightarrow \left( {\dfrac{4}{4} \times 11} \right) + \dfrac{3}{4}$
On simplifying the expression, we get:
$ \Rightarrow \dfrac{{44}}{4} + \dfrac{3}{4}$
Now, add the numerator over the common numerator.
$ \Rightarrow \dfrac{{44 + 3}}{4}$
$ \Rightarrow \dfrac{{47}}{4}$
Here also we will get the same solution i.e. the improper fraction is $\dfrac{{47}}{4}$.