Question

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

Answer 1

The above question is based on the concept of mixed fraction. The main approach towards solving this is by splitting it into terms in such a way that it reduces to normal fraction which is also called an improper fraction which has only numerator and denominator.

Complete step by step solution:
Mixed fraction is a combination of whole a whole number and a fraction. It is a form of a fraction which is defined as the ones having a fraction and a whole number. It can also be called a mixed number.

The expression is given as $1\dfrac{1}{2}$

Here, in this expression $1$ is the whole number and $\dfrac{1}{2}$ is the fraction.

An improper fraction is a fraction where the numerator is equal to or greater than the denominator.

So, the next step is to convert the mixed fractions to improper fractions. These improper fractions look like a mixed fraction without the whole number but having a fraction in it.
$\dfrac{2}{2} \times 1 + \dfrac{1}{2}$

In the above step, the fractions are generated in such a way that its division is 1 and also it adds with the fraction having the same denominator.
$\left( {\dfrac{2}{2} + \dfrac{1}{2}} \right) = \dfrac{3}{2}$

Therefore, the above fraction we get is called an improper fraction where the numerator is greater than denominator i.e., 3 is greater than 2.

Note: An important thing to note is that the numerator can never be smaller than the denominator for the fraction to be an improper fraction. If the numerator is smaller than the denominator then it is called a proper fraction.