Simplest Form Fractions Definition
When a fraction can’t be simplified further, it will be termed as the simplest form of that fraction. It means all those fractions are called simplest-form fractions when their numerators and denominators can’t be divided by a single divisor.
Note:
Read about a Fraction, Numerator, Divisor, and Denominator here.
For example, In 13/71 is the simplest form of a fraction because they are not divisible by the same number.
Table of Contents
Examples of simplest-form fractions
| Original Fraction | Simplest Form of a Fraction |
| 22/44 | 1/2 |
| 3/9 | 1/3 |
| 24/9 | 8/3 |
| 13/65 | 1/5 |
How to find the simplest form of a fraction?
Converting a given fraction into its simplest form is not a difficult task. You can follow two different methods to find the simplest form fractions. Here are those methods with brief guidance on how to do this.
Through simple division
When you have got a fraction, you can find its simplest form just with a simple division. You need to follow the upcoming steps for this task.
- Write the original fraction
- Find the HCF of the numerator and denominator
- Divide both (numerator & denominator) with HCF
- The resultant fraction will be the simplest form of the original fraction
Note:
Read about HCF here in detail.
Example 1:
Find the simplest form of 34/16.
Solution:
According to the above steps, we have to find the HCF of 36 and 16. For this, we have to find the common factors of both numbers. Let’s do it!
Factors of 34 = 2 x 17
Factors of 16 = 2 x 2 x 2 x 2
As we can see,
Common Factor = 2
So, we have to divide the numerator and denominator by “2”. After dividing, we get:
= 17/8
This is the simplest form of the fraction that we have found using HCF.
Note:
You can read about Common Factors here.
Using Ratio
In Mathematics, a fraction can be converted into a Ratio. To do this, you only have to write the numerator first and the denominator after the Ratio marks. Here are the steps to follow for converting a fraction into the simplest form through this method.
Note:
Read about Current Ratio here in detail.
- Convert the fraction into a Ratio format
- Start dividing using the smallest prime factor
- Keep dividing until you have found the numbers that are not divisible with the same divisor
- Convert that ratio into a fraction again by reversing the above conversion/li>
- You have got the simplest form of the fraction
Note:
You can read about Prime Factor here.
Example 2:
Find the Simplest form fraction of 28/44.
Solution:
Let’s convert this fraction into the Ratio format first.
28 : 44
These numbers can be divided by “2” because both are Even Numbers.
14 : 22
Again, these can be divided into “2”.
7 : 11
As both numbers are Prime Numbers, they can’t be divided further. Let’s convert them into a fraction again for getting the simplest form fraction.
= 7/11
Note:
You can read about Even and Prime Numbers here.
By following these methods, you can find the simplest form fractions of any complex fraction. It will help you in solving different Mathematical problems from a simple approach.
How to convert a decimal into the simplest fraction?
A decimal can also be converted into the simplest fraction. First of all, you need to write the decimal in the fraction format. To do so, you need to write the number in the numerator and put “1” in the denominator just below the Decimal point.
Count the numbers on the right side of the decimal and put equal numbers of “0s” just on the right side of the “1” in the denominator. Now, you have converted the decimal into a fraction. Here is how you can convert it into the simplest form fraction.
- Find the HCF of the numerator and denominator
- Divide both with that number
- The resultant fraction will be the simplest fraction of the given decimal
Example 3:
Find the simplest fraction of 0.44.
Solution:
First, we have to convert it into a fraction.
= 44/100
The HCF of 44 and 100 is “4”. By dividing them with 4, we get the following fraction.
= 11/10
This is the simplest fraction of 0.44 because these numbers can’t be divided with the same number.
FAQ's
How to find the simplest form of 90/25?
To find the simplest form fraction of 90/25, we need to find its HCF. The HCF is “5” and the simplest form of this fraction is 18/5.
Is 11/121 the simplest fraction?
The simplest fraction of 11/121 is 1/11.
Why these fractions are called simplest?
This type of fraction is called the simplest form fractions because they can’t be simplified further.
Can we find the simplest form of a fraction using LCM?
No, we can find the simplest form fractions using LCM. We need to find the HCF of the numerator and denominator to get the simplest fraction.
