Question

How do you write \[2\dfrac{1}{2}\] as an improper fraction?

Answer 1

Hint: In this question, we write a split mixed fraction into an improper fraction. To convert in improper fraction, first, we write a split mixed fraction in the form of the sum of a whole number and a fraction. After that, we will add the numbers by using the fraction addition rule.

Complete step by step answer:
In this question, the words improper fraction and split mixed fraction are used. First, we know about what is split mixed fraction and the improper fraction. We know what fraction number is. Fraction number is defined as the form which has the value in the numerator and the value in the denominator.
Split mixed fraction: the fraction which has a whole number and a fraction. The whole number and a fraction are writing together.
Let’s take an example. $a$ is the whole number and \[\dfrac{b}{c}\] is the fraction number then the split mixed fraction is written as \[a\dfrac{b}{c}\].
Improper fraction: the fraction which has the value in the numerator is greater than the value in the denominator is known as an improper fraction.
Let’s take an example. a is the value of numerator and b is the value of denominator, and a is greater than b. then the improper fraction is written as.
\[ \Rightarrow \dfrac{a}{b}\left( {where\;a > b} \right)\].
From the question, the split mixed fraction \[2\dfrac{1}{2}\] is given, which is converted to an improper fraction.
First, we write the split mixed fraction into the sum of the whole number and a fraction.
Then, \[2\dfrac{1}{2}\] is written as below.
\[ \Rightarrow 2\dfrac{1}{2} = 2 + \dfrac{1}{2}\]
Then, we write the whole number in the form of a fraction number as below.
\[ \Rightarrow 2 = \dfrac{4}{2}\]
Put that in the above number as
\[ \Rightarrow \dfrac{4}{2} + \dfrac{1}{2}\]
For adding two fractions, we add numerator to numerator. Denominators are common.
Then,
\[ \Rightarrow \dfrac{{4 + 1}}{2} = \dfrac{5}{2}\]

Therefore, the split mixed fraction \[2\dfrac{1}{2}\] can be written in the improper fraction as \[\dfrac{5}{2}\].

Note: As we know that if we want to convert a split mixed fraction to the improper fraction. First, you want to convert the whole number into fraction numbers. Then add two fractions. If the denominator is the same for both fractions, then you add both numerators and take the denominator as common.