Question

How do you write \[\dfrac{6}{10}\] in simplest form?

Answer 1

Hint: It is always better to look at the denominator first when we need to convert a fraction into a decimal. If a denominator only has $2$ and $5$ as prime factors, one way of writing a fraction as a decimal is to change the fraction so the denominator is a power of $10$. In case it has a prime factor other than $2$ and $5$, conversion to decimal could be longer and will result in an infinite loop with repeating decimals.
However, $10$ divide or multiply in the power of $10$, so that method will work here.

Complete step by step solution:
First reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of $6$ and $10$ using
$GCD(6,10)=2$
 \[\dfrac{6\div 2}{10\div 2}=\dfrac{3}{5}\] .

SInce, it can’t be solved further hence \[\dfrac{3}{5}\] is the required answer.

Note:
It is always better to look at the denominator first when we need to convert a fraction into a decimal. If the denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in the power of $10$. In case it has a prime factor other than $2$ and $5$, conversion to decimal could be longer and will result in an infinite loop with repeating decimals.