Question

What is \[1\dfrac{1}{4}\] as an improper fraction?

Answer 1

Hint: First we will see the two types of fractions, namely: - proper and improper fractions and understand their definition with the help of some examples. Now, to write the given mixed fraction into the improper fraction we will use the general formula of conversion given as: - \[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\].

Complete step by step answer:
Here, we have been provided with the mixed fraction \[1\dfrac{1}{4}\] and we are asked to convert it into an improper fraction. But first we need to know about the two different types of fractions: ‘proper fraction’ and ‘improper fraction’. So, let us see their definitions one – by – one.
1. Proper fraction: - A proper fraction is a type of fraction in which the numerator of the fraction is less than its denominator. For example: - \[\dfrac{9}{16},\dfrac{1}{7},\dfrac{101}{209}\] etc.
2. Improper fraction: - An improper fraction is a type of fraction in which the numerator of the fraction is greater than its denominator. For example: - \[\dfrac{7}{4},\dfrac{8}{15},\dfrac{99}{47}\] etc.
Now let us come to the question. We have the mixed fraction \[1\dfrac{1}{4}\]. Generally, if we have a mixed fraction of the form \[a\dfrac{b}{c}\], read as a whole b by c, then its meaning in mathematical form is given as: -
\[\Rightarrow a\dfrac{b}{c}=a+\dfrac{b}{c}\]
Taking L.C.M and simplifying we get,
\[\Rightarrow a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\]
\[\Rightarrow a\dfrac{b}{c}=\left( \dfrac{ac+b}{c} \right)\]
Here \[\left( \dfrac{ac+b}{c} \right)\] will be an improper fraction. Similarly, we can write \[1\dfrac{1}{4}\] as: -
\[\Rightarrow 1\dfrac{1}{4}=1+\dfrac{1}{4}\]
Taking the L.C.M which is 4, we get,
\[\begin{align}
  & \Rightarrow 1\dfrac{1}{4}=\dfrac{\left( 1\times 4 \right)+1}{4} \\
 & \Rightarrow 1\dfrac{1}{4}=\dfrac{4+1}{4} \\
 & \therefore 1\dfrac{1}{4}=\dfrac{5}{4} \\
\end{align}\]
Clearly we can see that in the above obtained fraction \[\dfrac{5}{4}\] the numerator 7 is greater than the denominator 4 so it is an improper fraction.

Hence, \[\dfrac{5}{4}\] is our answer.

Note: Remember that we don’t write proper fractions into mixed fractions because in such cases the quotient (a) is less than 1. You must remember the definition of the proper and improper fractions otherwise you may get confused. Remember the relation between a mixed fraction and the improper fraction given as: - \[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\].