Question

What is $5\dfrac{1}{3}$ as an improper fraction?

Answer 1

Hint: Here we have to convert the mixed fraction into improper fraction. Firstly we know that in improper fraction the numerator value is always greater than the denominator value. So by using the formula we will convert the mixed fraction into improper fraction and check for the condition stated and get our desired answer.

Complete step-by-step answer:
We have to convert $5\dfrac{1}{3}$ in an improper fraction.
The number $5\dfrac{1}{3}$ is a mixed fraction as it is a combination of the integer part which is $5$ and a proper fraction which is $\dfrac{1}{3}$ .
Here the proper fractions are those whose denominator value is greater than the numerator value.
 So we will use the below formula for converting it in improper fraction:
$x\dfrac{y}{z}=\dfrac{\left( x\times z \right)+y}{z}$……$\left( 1 \right)$
On comparing $5\dfrac{1}{3}$ by $x\dfrac{y}{z}$ we get,
$x=5,y=1,z=3$
Substitute the above value in equation (1),
 $\Rightarrow 5\dfrac{1}{3}=\dfrac{\left( 5\times 3 \right)+1}{3}$
$\Rightarrow 5\dfrac{1}{3}=\dfrac{15+1}{3}$
Simplifying further we get,
$\Rightarrow 5\dfrac{1}{3}=\dfrac{16}{3}$
We got the improper fraction as $\dfrac{16}{3}$ where our numerator value is greater than the denominator value.
Hence $5\dfrac{1}{3}$ as an improper fraction is $\dfrac{16}{3}$ .
So, the correct answer is “ $\dfrac{16}{3}$”.

Note: Fractions is defined as the part of a whole where the whole can be any number or a specific value. There are in total six types of fraction namely Proper fractions, Improper fractions, Mixed fractions, Like fractions, Unlike fractions, Equivalent fractions. Improper fractions are those whose numerator value is greater than denominator value and proper fractions are those whose denominator value is greater than the numerator value. Keep this difference in mind while solving such problems as one might get confused between the two definitions. Mixed fractions are made from the combination of an integer part and a proper fraction.