How do you simplify $\;30:75$?

Hint: Here the basic concept which is going to be used is finding GCF (Greatest Common Factor). After you will get the greatest common factor, just simply multiply it with the numerator and as well as with the denominator and you will get a reduced form.

Complete Step by Step Solution:
We can also write $30:75$ as $\dfrac{{30}}{{75}}$
This is a proper fraction. Since, the numerator is smaller than the absolute value of denominator, the fraction $\dfrac{{30}}{{75}}$ can be reduced
Now, we will find the GCF (Greatest Common Factor) that is the largest number which can divide 30 and 75 evenly
Factors of $30 = 1,2,3,5,6,10,15,30$
Factors of $75 = 1,3,5,15,25,75$
So, the GCF here is 15 as it is the largest number by which 30 and 75 can be divided without leaving any residue
Now, to simplify $\dfrac{{30}}{{75}}$ , just simply multiply numerator and denominator by 15
$=\left( {\dfrac{{30}}{{75}}} \right) \times \left( {\dfrac{{15}}{{15}}} \right)$
$=\dfrac{{30 \div 15}}{{75 \div 15}}$
On further simplification,
$=\dfrac{2}{5}$

Thus, $\dfrac{{30}}{{75}}$ is equivalent to $\dfrac{2}{5}$ in the reduced form
Hence $30:75 = 2:5$

Note:
There is an alternative method to solve this and these type of questions
We have numbered as $\dfrac{{30}}{{75}}$
First divide both the numerator and denominator by 3, we get $\dfrac{{10}}{{25}}$
Now, divide both numerator and denominator by 5, we get $\dfrac{2}{5}$
Since 2 and 5 are not divisible by any common number except 1, hence no further simplification is possible, so the answer is $\dfrac{2}{5}$.