 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says the following fractions represent just three different numbers separate them into three groups of equivalent fractions by changing each one to its simplest form. So first of all we change them into their simplest form and then we separate them into three groups of equivalent fractions. So let us start with the solution. Part A is 2 by 12. Now what we do here is first of all we divide the numerator and denominator of 2 by 12 by the hcf of 2 by 12, hcf of 2 and 12. We know that hcf of 2 and hcf of 12 is 2. So we divide the numerator denominator by 2 and that gives us 1 by 6. So now here we see that this cannot be reduced further. So in the simplest form 2 by 12 is nothing but 1 by 6. Let us see the B part now. The B part is 3 by 15. Again we do the same thing here. Here we divide the numerator and denominator by the hcf of 3 and 15. The hcf of 3 and 15 is 3. So we divide the numerator denominator by 3 and we will have 3 divided by 3 is 1 and 15 divided by 3 is 5. So the simplest form is 1 by 5. Now let us see the C part that is 8 divided by 50. Now here we see that 8 can be expressed as 2 into 2 into 2 and 50 can be expressed as 2 into 5 into 5. So in both of them we see that their highest common factor will be 2. So we divide the numerator and denominator of 8 by 50 by 2 dividing them by 2 we have. In the numerator we will have 8 divided by 2 is 4, 25 we have in the denominator. So but now we can see that we cannot reduce it further. So its simplest form is 4 by 25. We see that 4 by 25 becomes the simplest form because now we do not have any common factor in 4 and 25. So this becomes the simplest form of 8 by 50. Let us see the D part that is 16 by 100. Let us now find the hcf of 16 and 100. We see that 16 can be expressed as 2 into 2 into 2 because 2 2's are 4 2's are 8 2's are 16. Similarly 100 can be expressed as 2 into 2 into 5 into 5. 5 5's are 25 2 through the 4 so 25 into 4 is 100. Now we see here that the highest common factor is 2 into 2 that is 4. So we divide the numerator and denominator of 16 by 100 by 4 and that gives us 16 divided by 4 is 4 and 100 divided by 4 is 25. Now we see that there is no common factor between 4 and 25. So the simplest form is 4 divided by 25. Now we consider the e part that is 10 by 60. Now we see that the highest common factor of 10 and 60 is 10. So we divide the numerator and denominator by 10 and we get 10 divided by 10 is 1 and 60 divided by 10 is 6. Now we see that there is no common factor between 1 and 6 so this is the simplest form 1 by 6. Here we see that 1 by 6 is the simplest form because other than 1 we do not have any common factor between 1 and 6. Let us consider the h part that is 15 by 75. We see that the highest common factor of 15 and 75 is 15. So we divide the numerator and denominator by 15 and that gives us 15 divided by 15 is 1 and 75 divided by 15 is 5. So the simplest form is 1 by 5. Now we consider the g part that is 12 by 60. We divide again the numerator and denominator by their highest common factor that is 12. So when we divide the numerator and denominator by 12 we get 1 by 5 which is again the simplest form of 12 by 60. Now let us see the h part that is 16 by 96. We see that the h c f of 16 and 96 is 16. So we divide the numerator and denominator by 16 and that gives us 1 by 6. Here we see that this is the simplest form. Now let us consider the i part that is 12 by 75. The h c f of 12 and 75 is 3. So when we divide the numerator and denominator by 3 we get 4 by 25 which is the simplest form. Now we see the j part that is 12 by 72. We see the h c f of 12 and 72 is 12. So we divide the numerator and denominator by 12 and that gives us 1 by 6 which is the simplest form of 12 by 72. Now we consider the k part that is 3 by 18. We see that the h c f of 3 and 18 is 3. So we divide the numerator and denominator by 3 and that gives us 1 by 6 which is again the simplest form of 3 by 18. Now let us consider the l part that is 4 by 25. Now we see that there is no common factor between 4 and 25. So this is the simplest form. It cannot be reduced further. Now in all these parts we notice that each fraction is equal to either 1 by 6 or 4 by 25 or 1 by 5. So we have 3 groups formed now. The first group is part a, part e, part h, part j and part k because all of them they are equal to the fraction 1 by 6. The next group is b f g because all of them are equal to 1 by 5 and the last group is c d i l because all these fractions they are equal to 4 by 25 so this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.