Question

How do you write a mixed number in their lowest terms?

Answer 1

Hint: In this question we have to show how we can write a mixed number in its lowest form. A mixed number is also referred as a mixed fraction which is constituted of two parts, a whole number and fraction part. Converting a mixed fraction into its simplest form refers to converting it into an improper fraction and reducing it by dividing both the numerator and denominator by common factors. We will consider an example of a mixed fraction and then see how to convert it.

Complete step by step answer:
We have to convert a mixed number into its lowest terms. consider a mixed fraction $3\dfrac{2}{5}$.
We can see that $3$ in the given fraction is the whole number and $\dfrac{2}{5}$ is the fraction part.
We have to convert this mixed fraction to an improper fraction; an improper fraction is a fraction which only has a numerator and a denominator where the numerator is always greater than the denominator.
Now to convert the given mixed fraction:
 $\Rightarrow 3\dfrac{2}{5}$
The method over here is that we have to keep the denominator as it is, there will be changes in the numerator only while converting. We have to multiply the denominator of the fraction with the whole number and add whatever there is in the numerator, it can be written as:
$\Rightarrow 3\dfrac{2}{5}=\dfrac{(5\times 3)+2}{5}$
On simplifying the bracket, we get:
 $\Rightarrow 3\dfrac{2}{5}=\dfrac{15+2}{5}$
On simplifying the numerator, we get:
$\Rightarrow 3\dfrac{2}{5}=\dfrac{17}{5}$

Therefore, the mixed fraction $3\dfrac{2}{5}$ is equal to the improper fraction $\dfrac{17}{5}$, which is the required answer.

Note: If there are common factors in the numerator and denominator of a fraction, they should be cancelled out to simplify the fraction and to write it in its lowest terms. In the answer we can see that the numerator which is $17$,is greater than the denominator which is $5$ therefore, it satisfies the condition of being an improper fraction.
There is also a type of fraction called a proper fraction in which the numerator is lesser than the denominator for example:
$\dfrac{3}{7}$and $\dfrac{8}{13}$.