Rational Numbers are said to be in the lowest form if both the numerator and denominator have no other common factor other than 1. In other words, we can say that a Rational Number a/b is said to be in its simplest form if the HCF of a, b is 1 and a, b are relatively prime. To help you understand the concept better we have illustrated a few examples of how to convert Rational Numbers to their respective lowest form.
Example: 5/3 is a Rational Number in the Lowest Form or Simplest Form as it has no other common factors other than 1 Whereas, 14/21 is not in the simplest form as it has common factor 7 along with 1. Thus, it is not in the simplest form.
How to Convert a Rational Number to Lowest or Simplest Form?
Go through the below steps to change a Rational Number into its Lowest or simplest form. The Guidelines are along the lines
Step 1: Firstly, note down the rational number a/b given.
Step 2: Find the HCF of a, b
Step 3: If you get the HCF(a, b) i.e. k = 1 then they are in the simplest form.
Step 4: If at all the HCF(a,b) i.e. k ≠ 1 the simply divide both the numerator and denominator by k i.e. (a÷k)/(b÷k) to obtain the lowest form of rational number a/b.
Solved Examples
1. Determine whether the following rational numbers are in their lowest form or not?
(i)14/81 (ii) 72/24
Solution:
1/81 is in its lowest form as the HCF is 1 i.e. both the numerator and denominator have no common factors other than 1.
(ii) 72/24
72 = 2 × 2 × 2 × 3 × 3, 24 = 2 × 2 × 2 × 3
HCF of 72, 24 is 24
Therefore, the rational number 72/24 is not in the lowest form.
2. Express 45/30 in its simplest form?
Solution:
We have 45/30
Find the HCF of 45, 30 initially
HCF(45, 30) = 15
As the HCF is not equal to 1 simply divide the numerator and denominator of the given rational number with 15.
45/30 = (45÷15)/(30÷15) = 3/2
Therefore, 45/30 in its simplest form is 3/2.
3. Express the Rational Number 36/24 into its Lowest Form?
Solution:
Given Rational Number 36/24
Figure out the HCF(36, 24) at first
HCF(36, 24) = 12
Since HCF is not equal to 1 divide both the numerator and denominator with the HCF obtained.
36/24 = (36÷12)/ (24÷12)
= 3/2
Therefore, 36/24 expressed into its lowest form is 3/2.
4. Reduce 3/15 to its Lowest Form?
Solution:
Given Rational Number is 3/15
Find out the HCF(3,15)
HCF(3,15) = 3
As the HCF isn’t equal to 1 divide the numerator and denominator of rational number with HCF to change it to the lowest form.
3/15 = (3÷3)/(15÷3)
= 1/5