 Hello and welcome to the session. In this session, we shall write, interpret and explain statement of order for rational numbers in real-life context. Let Larry and Sandra distribute sweets in themselves and Larry and Sandra both get half of the sweets. Can we say anything about the amount of share? We can say that they both received equal amount of sweets because Larry got half of the sweets that was 1 by 2 which is equal to 0.5 and Sandra got half of the sweets that was also 1 by 2 which is equal to 0.5. So we can say that the fraction is same but if Larry gets one-third of the sweets and Sandra gets two-third of the sweets, now what can we say about their share? For this, we shall compare an other diffractions with the help of number line. Since we have 3 in the denominator, so we divide unit in 3 parts on the number line and we have 0 by 3, 1 by 3, 2 by 3 and 3 by 3. 0 by 3 is 0, then 1 by 3, 2 by 3 and 3 by 3 is 1 and now we plot 1 by 3 and 2 by 3 on the number line. Now we see that 2 by 3 is on the right side of 1 by 3. So 2 by 3 is greater than 1 by 3 and we write 2 by 3 is greater than 1 by 3. So we can interpret that Sandra has more sweets than Larry. Let us consider an example. 30 out of 36 girls and 34 out of 40 boys went on an abutational trip. We went to find whose greater fraction went on the trip where fraction of girls is 30 by 36 and fraction of boys is 34 by 40 and we can find the greater fraction with the help of a number line. Whenever we have different enlarged values in denominator, it is always convenient to convert the fraction into a decimal number. So 30 by 36 will be equal to 5 by 6. Now we divide 5 by 6 since 5 is smaller than 6. So we put a decimal in quotient and mx0 and now we have 6 into 8 is 38 and we get the remainder as 2. Now 2 is smaller than 6. So we mx1 by 0 and we get 20 and now 6 into 3 is 18 and again we get the remainder as 2. So we mx1 by 0 and we get 20. Now 6 into 3 is 18 and we get 2 as remainder. It means we are having a repetition of 2 so the division is endless and thus the digit 3 in quotient repeats. So it is a non-terminating decimal and we write 5 by 6 as 0.8333 and so on which can also be written as 0.83 by and therefore we get the fraction 30 by 36 is equal to 0.83 by and 34 upon 30 can be written as 17 by 20 which I am division this 0.85 the decimal I have expressed in tenths so we divide the number line between 0.80 and 0.90 in 10 parts. Now 0.83 by will be equal to 0.83333 and so on and this will lie in between 0.83 and 0.84 and this is slightly greater than 0.83 so we plot it both and we also put point at 0.85 from the number line we see that 0.85 is to be right of 0.83 by so we can say that 0.85 is greater than 0.83 by thus we conclude that the greater fraction as boys went to the trip thus with the help of ordering the rational numbers we can predict and draw conclusions. Let us consider one more example. The following table shows the attendance of the school carnival which grade has the greatest and least fraction of attendance. For grade 5 the attendance is 5 upon 8 for grade 6 is 0.5 and for grade 7 is 583 upon 1000. First of all we shall write these fractions in decimal form and then we shall plot these points on the number line. So 5 by 8 can be written as 0.625 when 5 is divided by 8 we get 0.625 and 583 by 1000 can be written as 0.583. In grade 5 and 7 we have 3 decimal places and for grade 6 it is 0.5 since putting as many zeros after decimal does not make any difference so we can write 0.5 as 0.500. Now we shall plot these points on the number line. Now the gap between 0.625 and 0.583 is large enough so we will choose the scale of the number line accordingly. Here we will take difference of 0.025 between numbers. Let us make the number line. Now we shall plot these points on the number line. For grade 5 we have the attendance as 5 upon 8 which is equal to 0.625 so we plot it here. For grade 6 it is 0.500 and here is the point. For grade 7 we have the attendance as 0.583 and 0.583 will lie in between 0.575 and 0.600 so we mark it here. From the number line we can see that fraction of grade 5 students is on the right of both grade 6 and grade 7. So grade 5 the greatest part of class participating in the carnival also grade 6 is on the left of both grade 7 and grade 5. So grade 6 has the least part of class participating in the carnival. We can also write the order from least to greatest 0.500 is less than 0.583 is less than 0.625 which is equal to 0.5 is less than 583 upon 1000 is less than 5 by 8 or it can also be written as grade 6 is less than grade 7 and is less than grade 5. So we plot that grade 5 has the greatest part of class participating in the carnival and grade 6 has the least part of class participating in the carnival. This completes our session. Hope you enjoyed this session.