Question

How do you simplify the fraction $ \dfrac{3}{{15}} $ ?

Answer 1

Hint: A fraction is known as the division of a whole thing into equal parts. The conversion of a fraction into the simplest form is known as its simplification; it is done to make the calculations easier. We divide both the numerator and the denominator by their common divisor to simplify the fraction. This way, we can find the correct answer.

Complete step-by-step answer:
In the given question, the term in the numerator is “3” which is a prime number and the denominator is “15” which is a product of prime numbers 3 and 5, after dividing the numerator and denominator by the common factor 3, we get the fraction as $ \dfrac{1}{5} $ , now both numerator and denominator are prime numbers so the fraction is in simplified form and cannot be simplified further.
We have to simplify the fraction $ \dfrac{3}{{15}} $
So to simplify them we write both the numerator and denominator as a product of prime factors, as follows –
 $ 3 = 3 $ as it is itself a prime number.
 $ 15 = 5 \times 3 $
We see that 3 and 15 have common factor 3, so we divide both of them by 3 –
 $ \dfrac{{\dfrac{3}{3}}}{{\dfrac{{15}}{3}}} = \dfrac{1}{5} $
Hence, the simplified form of fraction $ \dfrac{3}{{15}} $ is $ \dfrac{1}{5} $ .
So, the correct answer is “$ \dfrac{1}{5} $”.

Note: For simplifying a fraction, we divide both the numerator and denominator by their common factors till the common factor is 1. But if the numerator and the denominator both are prime numbers, then the common factor of the numerator and the denominator will be one (as the prime numbers are the numbers that are only divisible by one and itself).