Question

How do you write \[5\dfrac{3}{4}\] as an improper fraction?

Answer 1

Hint: First understand the types of fractions, namely: proper and improper fractions by taking some examples. Now, to write the given mixed fraction \[5\dfrac{3}{4}\] use the formula: - \[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\], to change it into the improper fraction.

Complete step by step solution:
Here, we have been provided with the mixed fraction \[5\dfrac{3}{4}\] and we are asked to convert it into an improper fraction. But first we need to know about the terms ‘proper fraction’ and ‘Improper fraction’. So, let us see their definitions one – by – one.
1. Proper fraction: A proper is a type of fraction in which the numerator of the fraction is less than its denominator. For example: - \[\dfrac{3}{4},\dfrac{4}{9},\dfrac{12}{35}\] 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 examples: - \[\dfrac{5}{3},\dfrac{9}{7},\dfrac{11}{10}\] etc.
Now, let us come to the question. We have the mixed fraction \[5\dfrac{3}{4}\]. 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: -
\[\Rightarrow a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\]
\[\Rightarrow a\dfrac{b}{c}=\left( \dfrac{ac+b}{c} \right)\]
Here, \[\left( \dfrac{ac+b}{c} \right)\] will be an improper fraction. Now, \[5\dfrac{3}{4}\] can be written in a similar way as: -
\[\Rightarrow 5\dfrac{3}{4}=5+\dfrac{3}{4}\]
Taking the L.C.M. which is 4, we get,
\[\begin{align}
  & \Rightarrow 5\dfrac{3}{4}=\dfrac{\left( 5\times 4 \right)+3}{4} \\
 & \Rightarrow 5\dfrac{3}{4}=\dfrac{20+3}{4} \\
 & \Rightarrow 5\dfrac{3}{4}=\dfrac{23}{4} \\
\end{align}\]
Clearly, we can see that in the above obtained fraction \[\dfrac{23}{4}\], the numerator 23 is greater than the denominator 4, so it is an improper fraction.
Hence, \[\dfrac{23}{4}\] is the required answer.

Note: You must remember the definition and examples of the proper and improper fraction otherwise you may get confused. Remember that 1 is called unit fraction.
Remember the relation between a mixed fraction and the improper fraction given as: \[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\]. These conversions are used in topics like ratio and proportion, percentage where we are generally given information in mixed fractions. Here, we convert them into improper fractions for the calculations.