Question

How do you write $\dfrac{6}{60}$ in simplest form?

Answer 1

Hint: In order to solve this question, we need to reduce it to a form such that the numerator and the denominator have no factors common. We do this by calculating the Greatest Common Divisor (GCD) of both the numerator and denominator. We then divide both the numerator and denominator by this Greatest Common Divisor (GCD) to get the simplest form of the given question.

Complete step by step solution:
We are required to find the simplest form of the term $\dfrac{6}{60}.$ In order to do this we calculate what is known as the Greatest Common Divisor (GCD) of the numerator and denominator.
The Greatest Common Divisor (GCD) of any two terms is defined as the largest number or integer which can divide both the terms. So now in this case, we can take those two numbers as 6 and 60 which are nothing but the numerator and denominator of the term in the given question.
$\Rightarrow GCD\left( 6,60 \right)$
We first show all the factors of both the numerator and denominator.
Factors of 6 are: 1, 2, 3 and 6.
Factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12,15, 20, 30 and 60.
We can see that the highest factor that is common in both is 6. Therefore, this is the GCD.
$\Rightarrow GCD\left( 6,60 \right)=6$
We now need to divide both the numerator and denominator by the factor 6.
$\Rightarrow \dfrac{6\div 6}{60\div 6}$
We simplify the numerator and denominator by cancelling the terms. We then represent the simplified form as:
$\Rightarrow \dfrac{1}{10}$
This is the simplest form of the given question. We can also represent this in the decimal form as,
$\Rightarrow \dfrac{1}{10}=0.1$
Hence, we can represent $\dfrac{6}{60}$ in its simplest form as $\dfrac{1}{10}.$

Note: To answer this question, students are required to have a good knowledge in the factorization of terms and also know the tables very well. We can also solve this question by prime factorization method, in which we divide the numerator and denominator by the same common prime factor till we can no longer divide the terms.