 Hi and welcome to the session. Today we will learn how to compare fractions. First of all let us see how to compare like fractions. We already know that like fractions are the fractions with same denominator. So suppose we are given two fractions 5 by 9 and 7 by 9 and we need to compare these two fractions. Now in like fractions the fraction with greater numerator is greater. So from this we can say that 7 by 9 is greater than 5 by 9 because the numerator 7 is greater than the numerator 5. Now let's see how to compare unlike fractions with same numerator. We are given two fractions 5 by 9 and 5 by 7. Now in such a case fraction with smaller denominator is greater. So this implies 5 by 7 is greater than 5 by 9 because the denominator 7 is smaller than the denominator 9. Now let's see how to compare unlike fractions with different numerator. Suppose we are given two fractions 3 by 5 and 2 by 3. These are unlike fractions. Now we already know how to compare like fractions that is the fractions with same denominator. So let's try to change the denominators of the given two fractions so that they become equal and for this we will use the method of equivalent fractions. Now for this purpose first of all we will find the LCM of the denominators of both the fractions. So LCM of is equal to 5. So now we will change the denominators of both the fractions to 15. The equivalent fraction of 3 by 5 such that the denominator 5 becomes 15. So we will multiply the numerator and denominator by 3 and we will get 9 by 15. Now let's find the equivalent fraction of 2 by 3. Multiply the numerator and denominator by 5 and we will get 10 by 5. So the fraction with greater numerator will be greater that means 10 by 15 is greater than 9 by 15 or this implied 3 is greater than 3 by 5. Now let's move on to our next topic addition and subtraction of fractions. Now let us see addition or subtraction of like fractions. Suppose we are given two fractions 2 by 9 and 5 by 9 and these two fractions then will be equal to in denominator we will take 9 which is common to both the fractions and in numerator we will take 2 plus 5. So this will be equal to 7 by 9. Now if we have then this will be equal to in denominator we will take 9 and in numerator we will subtract 2 from and we will get 3 by 9. Next we have addition or subtraction of unlike fractions 4 by 5 and 2 by 3 and we want to add these two fractions, two fractions are unlike fractions. So we will try to change the denominators of the given fractions such that they become equal and for this we will use the method of equivalent fractions. So for this first of all let us take the LC and LCM of 5 and 3 is equal to 15. Now we will find the equivalent fractions of 4 by 5 and 2 by 3. Now 4 by 5 is equal to 12 by 15 and 2 by 3 is equal to 10 by 15. So plus 2 by 3 is equal to 12 by 15 plus 10 by 15. Now these are like fractions and we already know how to add like fractions. So this will be equal to 22 by 5. Now let's move on to addition or subtraction of mixed fractions. Suppose we are given the fractions 1 1 by 3 and 3 2 by 3 and we want to add these two fractions. Now there are two ways to add mixed fractions. Let's see the first way of adding them. We have 1 1 by 3 plus 3 2 by 3. Now the mixed fraction can be written as the whole part plus the proper fraction. So we can write this as 1 plus 1 by 3 plus 3 plus 2 by 3. Now first of all we can add 1 and 3 and we will get 4 plus 1 by 3 plus 2 by 3. We can add separately. So we get plus 1 by 3 plus 2 by 3 is equal to 3 by 3 and this is equal to 4 plus 1 which gives us the second way of adding mixed fractions 1 1 by 3 plus 3. Now first of all we will change these both mixed fractions to improper fractions. So we will get 4 by 3 plus 11 by 3 equal to 15 by 3 which is equal to 5 in its lowest for how we can add mixed fractions. With this we finished this session. Hope you have understood all the concepts. Goodbye, take care and keep smiling.