Question

How do you write the fraction \[\dfrac{5}{{15}}\] in simplest form?

Answer 1

Hint: Here, we have to use the concept of the factorization. First, we will rewrite the numbers in the numerator and the denominator of the given fraction in their factor form. Then we will cancel out the common terms to get the simplified form of the given fraction.

Complete step by step solution:
The fraction is \[\dfrac{5}{{15}}\].
First, we will write the factors of the numbers in the numerator and denominator.
Factorization is the process in which a number is written in the form of its small factors which on multiplication give the original number.
Therefore, we get the fraction in the form of the factors of the numbers
\[\dfrac{5}{{15}} = \dfrac{{1 \times 5}}{{3 \times 5}}\]
Now we will cancel out the common terms present in the numerator and the denominator of the fraction. Therefore, we get
\[ \Rightarrow \dfrac{5}{{15}} = \dfrac{1}{3}\].

Hence the simplified form of the given fraction \[\dfrac{5}{{15}}\] is \[\dfrac{1}{3}\].

Note: We know that there are three main types of fraction i.e. proper fractions, improper fractions, and mixed fractions.
Proper fractions are a fraction having the numerator less, or lower in degree, than the denominator. The value of proper fraction after simplification is always less than 1.
An improper fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction. After the simplification of an improper fraction results in the value which is equal or greater than 1, but not less than 1.
A mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction. After the simplification of a mixed fraction results in the value which is always greater than 1. An improper fraction can be converted into a mixed fraction.