 Let's talk about simplest form of fraction. Let's take these two fractions 16 by 40 and 10 by 25. Now we know about equivalent fractions So if we divide or multiply in numerator and denominator by the same number We get the equivalent fraction, which is equal to the original fraction Now when we want to find the simplest form of fraction We divide the numerator and denominator by a common number or the same number and arrive at certain fraction and the objective is to reach a fraction in which you find numerator and denominator in a way that they do not have common factor other than one. So if we divide 16 and 40 by 8 we get 2 by 5 and 2 and 5 do not have a common factor other than 1 and therefore this is a simplest form of fraction Now we can do the same thing for 10 by 25 and we can decide to divide both of these by 5 But in the fraction above we had decided to divide it by 8. Here we have decided to divide it by 5 How do we know by which number do we have to divide to get the simplest form? It's a trial and error at the start but once you start practicing more and more You will start seeing the common factors of numerator and denominator very quickly And then if you keep dividing you will arrive At the simplest form for example, if we just take 16 by 40 again So This 16 by 40 if you are not sure we definitely know that both are even numbers. So we can divide Both of these by 2 And we can arrive at a fraction something which looks like this 8 by 20 Again, both of these are divisible by 2. So let me just divide it again by 2 And I get 4 by 10 I can keep dividing by 2 until I can and I get 2 by 5 So after multiple steps, I reached 2 by 5 So it's it's all right if you reach the simplest form of fraction after some steps But if you keep seeing some other factors of numerator and denominator, which can divide Both of them then keep on dividing and reach a point where now you cannot divide numerator and denominator by any common factor other than 1 And then you arrive at the simplest form Let's take one more example So we have 21 by 56 and now to get this simplest form Let's first see how we can write 21 in different ways By doing that, we will know what are different factors of 21 same thing for 56 we can write it as 7 times 8 Now the common thing that you see for both of them is 7 and we will divide Both of these numerator and denominator by 7 If we divide 21 by 7 we get 3 in the numerator and in the denominator we get 8 Now if we write 3 again and see how we can write it We can write it as 4 times 2 or 2 times 2 times 2 whatever but there is no common factor now other than 1 one is the only common factor for 1 and 8 And now this is the simplest form Simplest form we are looking for let's take one more quick example So if we have 30 by 66, how can we write 30 and 66 we can write 30 As 6 times 5 and we can write 66 as 6 times 11 And an easy way to find the simplest form is to just cancel out the common factors from numerator and denominator now you can also write 30 by 66 as 30 divided by 6 And 66 divided by 6 because you know that 6 is a common factor And once you do that you get 5 divided by 11. This is the same thing here And is is there any factor that divides 5 and 11? No, and that's why this is a simplest form now What about 20 divided by 10 now You can directly divide 20 by 10. So basically 20 divided by 10 and in the denominator as well You will have 10 divided by 10 You get 2 over 1 which is nothing but 2. So you don't really have to write the denominator, but there is no common factor for 2 and 1 other than 1. So 2 is the simplest form of the fraction here So whenever you reach a point by dividing numerator and denominator by common factors And you reach a point where the numerator and denominator Do not have any common factor other than 1 you have reached the simplest form