Question

How do you write $5\dfrac{1}{2}$ as an improper fraction?

Answer 1

Hint: To write the given number $5\dfrac{1}{2}$ into an improper fraction, we are going to multiply 2 by 5 first and then add the result of this multiplication with 1 and write this addition in the numerator in the final expression and the denominator is 2 in the final expression.

Complete step by step answer:
The number given in the above problem which we have to write in the improper fraction as follows:
$5\dfrac{1}{2}$
To convert the above expression into an improper fraction we are going to put an addition sign between 5 and $\dfrac{1}{2}$ which will look as follows:
$5+\dfrac{1}{2}$
Now, we are going to multiply 2 by 5, and then we are going to add the result of this multiplication into 1 and that will be the numerator of the final expression and the denominator is 2 in the final expression.
$\dfrac{5\left( 2 \right)+1}{2}$
Multiplying 5 by 2 in the numerator of the above expression will give 10 so writing 10 in place of $5\left( 2 \right)$ in the above expression and we get,
$\dfrac{10+1}{2}$
Now, when the expression written in the numerator of the above expression gets added then the result of this addition is 11 so writing 11 in place of $\left( 10+1 \right)$ in the above expression we get,
$\dfrac{11}{2}$

From the above, we have determined the improper fraction of the given expression which is equal to $\dfrac{11}{2}$.

Note: From the above problem, we have learned how to convert the expression in the following form into an improper fraction.
The expression should be in the form which is given in the above problem:
$5\dfrac{1}{2}$
The similar forms which can be possible are as follows:
$2\dfrac{2}{3},4\dfrac{5}{6}$
The important point to be noted is that improper fraction is the fraction in which the numerator is always greater than the denominator whereas, in the proper fraction, the numerator is lesser than the denominator.