Question

How do you write the fraction $\dfrac{{12}}{{36}}$ in simplest form?

Answer 1

Hint: A fraction is said to be in its simplest form when the numerator and denominator is not a common factor which can divide both the numerator and the denominator. Also the common factor should be a whole number, because dividing with decimal number or fraction will complex it more instead of converting it in simplest form.

Complete answer:
 To simplify fractions we have to find the Highest Common Factor (HCF) of the numerator and denominator in order to divide them with that number (HCF).
So let us find the highest common factor a between the numerator $(12)$ and the denominator $(36)$
$
  12 = 2 \times 2 \times 3 \\
  36 = 2 \times 2 \times 3 \times 3 \\
 $
Therefore highest common factor of $(12)$ and $(36)$ comes out to be $2 \times 2 \times 3$ that is equal to $12$
Now dividing both the numerator and the denominator by $12$,
\[
  \dfrac{{12 \div 12}}{{36 \div 12}} = \dfrac{1}{3} \\
    \\
 \]
\[\therefore \dfrac{1}{3}\] is the simplest form of the fraction $\dfrac{{12}}{{36}}$

Note: Alternative method: You can convert a fraction into its simplest form by one more method that is by continue division of the numerator and the denominator with prime numbers $(2,\;3,\;5,\;7,\;13.....)$ until they does not have any common factor left except $1$
Let us understand this by above example $\dfrac{{12}}{{36}}$
Dividing $12$ and $36$ with prime numbers starting with $2$ and going on further $(2,\;3,\;5,\;7,\;13.....)$ until they do not have any common factor left.
\[\dfrac{{12 \div 2}}{{36 \div 2}} = \dfrac{{6 \div 2}}{{18 \div 2}} = \dfrac{3}{9}\]
Now we can’t further divide it by \[2\] so we try to divide with next prime number which is $3$
\[\dfrac{{3 \div 3}}{{9 \div 3}} = \dfrac{1}{3}\]
Now they do not have any common factor left except one. So answer is $\dfrac{1}{3}$
This is a lengthy process, better go with the upper one.