 Hello and welcome to this session. In this session, we are going to discuss comparison of two fractions on a number 9. Now let us compare which fraction is greater minus 4 and 5 by 6 or minus 4 and 1 by 6. Now the mixed fraction minus 4 and 5 by 6 is equal to minus 29 by 6 which is equal to 4.833 and so on. And the mixed fraction minus 4 and 1 by 6 is equal to minus 25 by 6 which is equal to 4.166 and so on. This means both these fractions line between minus 4 and minus 5. Now here the denominator of both these fractions is 6. So we will divide the number line between minus 4 and minus 5 into 6 equal parts. Now if we had to take fractions with denominator 6 between 0 and 1 then there will be 0 minus 1 by 6 minus 2 by 6 minus 3 by 6 minus 4 by 6 minus 5 by 6 and minus 6 by 6 which is equal to minus 1. So here we can divide the number line between 0 and minus 1 into 6 equal parts. Similarly if we had to take fractions with denominator 6 between minus 2 and minus 1 then there will be now minus 1 can be written as minus 6 by 6 that is here the denominator is 6 then the next fraction will be minus 7 by 6 then the next fraction will be minus 8 by 6 the next fraction will be minus 9 by 6 then minus 10 by 6 minus 11 by 6 and minus 12 by 6 which is equal to minus 2 or we can write it as minus 1 then minus 7 by 6 can be written as minus 1 and 1 by 6 then minus 8 by 6 can be written as minus 1 and 2 by 6 and so on. So we have written these fractions in the form of mixed fractions between minus 3 and minus 2 we can write the fractions as minus 2 then minus 2 and 1 by 6 then minus 2 and 2 by 6 then minus 2 and 3 by 6 minus 2 and 4 by 6 minus 2 and 5 by 6 and minus 3 now let us write the fractions between minus 5 and minus 4 and these fractions will be minus 4 minus 4 and 1 by 6 minus 4 and 2 by 6 minus 4 and 3 by 6 minus 4 and 4 by 6 minus 4 and 5 by 6 and minus 5 so in this way we can represent these fractions in between minus 4 and minus 5 on the number line now let us write these two fractions on the number line now this is the first 5 by 6 now on the number line numbers on the right side are greater and numbers on the left side are smaller now where on the number line you can see minus 2 to the right so in 5 by 6 therefore another way of representing rational numbers on a number line is to convert 1 into decimal on the graph in 10 equal parts on a number line we have the numbers like 0, 0.1, 0.2 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.91 and so on this we have divided the number line between 8 and 9 into 10 equal parts we will move 4 parts to the right of 8 reach at this point which represents the number 1 let us discuss one example now where we have to see that which fraction is greater 1 by 2 or 4 by 5 now 1 by 2 is equal to 0.5 and 4 by 5 is equal to 0.8 so where also we have drawn a number line in which we have divided each unit into 10 equal parts 0.5 and 0.8 on the number line 0.8 on the number line which means 0.5, 0.2 and 0.8 is the fraction 4 by 5 the way is to divide of 1 by 2 which means 1 by 2 so we can easily compare fractions by using number line we can plot fractions in decimal form vertically on the number line the numbers above 0 are positive and numbers below 0 are negative now suppose if we have to plot minus 1.2 on the number line then we will move minus 1 which represents minus 1.2 on the number line now suppose we have to plot minus 4.5 on the vertical number line now we will get minus 4.5 lies between minus 4 and minus 5 so for rotating the point minus 4.5 on the number line we will move below minus 4 on the number line and we will reach at this point and this point represents minus 4.5 on the vertical number line now suppose we have to compare which fraction is greater minus 31 by 10 or minus 41 by 10 then we can also compare this by using a vertical number line now minus 31 by 10 is equal to minus 3.1 minus 41 by 10 is equal to minus 4.1 locate these points on the number line now this is the point minus 3.1 and this point represents minus 4.1 now on a vertical number line the numbers above are greater and the numbers below are smaller now here minus 3.1 is above the number minus 4.1 therefore minus 3.1 is greater than minus 4.1 which means the fraction minus 31 by 10 is greater than the fraction minus 41 by 10 so in this session you have learnt how to compare two fractions on a number line and this completes our session hope you all have enjoyed the session