Question

How do you write the fractions as a sum of unit fractions: \[5/12\]?

Answer 1

Hint: Here, we will rewrite the given fraction in the form of the sum of Unit fractions. We will write the given fraction in the form of unit fractions and then by adding the unit fraction of the given fraction, we will get the sum of the unit fractions of the given fraction.

Complete Step by Step Solution:
We are given a fraction \[5/12\].
Now, we will denote the given fraction in the form of unit fraction, we get
\[\dfrac{5}{{12}} = \dfrac{1}{{12}} \times 5\]
Now, we will denote the given fraction in the form of the sum of the unit fraction, we get
\[ \Rightarrow \dfrac{5}{{12}} = \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}}\]

Therefore, the fractions \[\dfrac{5}{{12}}\] can be denoted as the sum of unit fraction as \[\dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}}\].

Additional information:
We should know that a unit fraction is defined as a fraction whose numerator is always 1 and the denominator is always a Positive Integer. A unit fraction is,
therefore, the reciprocal of the positive integer. We will prove that the sum of the unit fractions as a given fraction.

Note: We know that if a fraction is denoted in the form of unit fractions, then we should be careful that for a given same fraction, the sum of all the unit fractions has the same denominator as the given fraction. Thus, the sum of the unit fractions is the same as the sum of the like fractions. We found that the sum of the unit fraction is \[\dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}}\] for the given fraction \[\dfrac{5}{{12}}\].
We can add the like fractions by adding the numerators since the denominators are the same.
\[ \Rightarrow \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} = \dfrac{{1 + 1 + 1 + 1 + 1}}{{12}}\].
\[ \Rightarrow \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} + \dfrac{1}{{12}} = \dfrac{5}{{12}}\].