 Hello and welcome to the session. In this session we will learn how to add and subtract rational numbers. Now we know that a rational number is a fraction, for example 1 by 2, 3 by 1, 4 by 2, 1 by 5 and so on are all rational numbers. Here we will learn adding and subtracting fractions with like denominators, fractions with unlike denominators and decimals. Before learning how to add and subtract fractions, let us recall some rules to add and subtract integers. If we have to add two positive integers, then we will add the two integers and give positive sign to the result. For example, consider the two integers plus 2 and plus 3. Now on addition, these two integers will give plus 5. So here we have added the two integers and gave positive sign to the result. The second rule is if we have to add two negative integers, then in this case we will add the two negative integers and give negative sign to the result. For example, minus 2 the whole plus or minus 3, that is we are adding two negative integers. So its result will be minus 5, that is we have added the two integers which is 2 plus 3 equal to 5 and we gave negative sign to the result. Then in the third rule, if we have to add two integers with opposite sign, then in this case we subtract these two integers. Now here consider the two integers plus 2 and minus 3. Now we have to add them. So in the first step, we will subtract these two integers, that is 3 minus 2 is equal to 1 and we will give the sign of the larger number to the result. Now here 3 is greater than 2 and you can see that there is a negative sign with 3. So in the answer, we will get the negative sign with 1. So the answer is minus 1. Minus 2 plus of plus 3 will give the answer as 1. Now let us learn the addition and subtraction of fractions having like denominator. Now the fractions having like denominators, we need the fractions having same denominator. For example 2 by 5 and 3 by 5 are the fractions with like denominator as the denominator in both the fractions is same that is 5. First of all let us learn the addition of two fractions with same denominators. Now suppose if we have to add 2 by 5 and 3 by 5 which are the fractions with same denominators, then in this case we will add the numerators and write the sum over the denominator. Now here the sum of the numerators will be 2 plus 3 upon the denominator is 5. So this is equal to 5 upon 5 which is equal to 1. Now here when we add the numerator we follow the same rules of addition we have mentioned earlier. Now suppose if we have to add 1 by 11 and minus 3 by 11 now 5 by 11 plus of minus 3 by 11 will be equal to add the numerators that is 5 plus of minus 3 whole upon the denominator which is 11. So this is equal to now by using the third rule of addition we have 5 plus of minus 3 equal to 2 and the denominator is 11. So in the numerator we have 2 and in the denominator we have 11. Now let us add extra fractions with same denominators. Now here we have minus 2 and 3 by 8 plus of minus 3 and 7 by 8 these extra fractions into intercom fractions. Now 8 into 2 is 16 and 16 plus 3 is 19. So this is equal to minus 19 upon 8 plus of minus and here it will be minus 31 upon 8. Now again we will apply the same rule which we have discussed earlier. Here in the numerator we will have minus 19 plus of minus 31 upon 8 by using the second rule of addition and subtraction of integers. In the numerator we will have minus 19 plus of minus 31 which is equal to minus 15 and in the denominator we will have that is here we have added the two integers that is 19 plus 31 which is 15. The answer we gave the negative sign into 4 is 8, 2 into 25 is 50. So this is equal to minus 25 upon 4 and in next fraction this will be minus 6 and 1 upon 4. The subtraction of the fractions will be like denominators. Here we have to subtract 4 by 7 from 2 by 7 that is 2 by 7 minus 4 by 7. Now here in this case we will subtract the numerator and write the difference over the denominator. So this is equal to 2 minus 4 4 upon 7 minus 4 is equal to minus 2, that is plus into minus is minus then plus into plus is plus is plus and minus into plus is again minus. We have to subtract minus 3 upon 7 from minus 2 and 1 by 7. In the first step let us convert the mixed fraction into improper fashion. So this is equal to minus 15 upon 7 minus of minus 3 upon 7. Further this is equal to minus 15 upon 7. Now here we will use the third rule to be equal to minus of minus which is the upon 7. Now here these two shows with same denominators. So again we will follow the same procedure which we have discussed earlier. In the numerator we will have minus 15 plus 3. All upon in the denominator we will have 7. So this is equal to upon 7. So in mixed fraction we can write it as minus 1 and 5 upon 7 the addition and subtraction of unlike fractions. Fractions are the fractions with different denominators. For example 3 by 5 by 10. Here the denominators are 5 and 10 which are different. Now first of all let us add 3 by 5 and 7 by 10. We will convert these two unlike fractions into like fraction and the ncm of the denominators which is equal to 10. Now we know that 5 into 2 is 10. Now we will make the denominator of the fraction 3 by 5 is equal to 10 for this and divide this fraction by 2. So it will be equal to 6 by 10. Now 3 by 5 plus 7 by 10 is equal to 6 by 10 plus 7 by 10. So we have converted these two fractions into like fractions so we can easily add them by using the rules which we have discussed earlier. So this will be equal to fraction this is equal to 1 and 3 by 10. We can also subtract 2 unlike fractions by making the denominators same. The addition and subtraction of decimals. Now we can add and subtract the decimals in the same way as we do with the whole numbers the decimal point. Now let us do the following example in which we have to find minus 4.05 plus 7.62. These two numbers are of opposite sign so we have to subtract. So here we will subtract 4.05 from 7.62 and here we have written these two numbers in such a way that the decimal point is lined up and subtracting this is equal to 3.57 and in the answer we will put the sign of the larger number which is a positive sign. So its answer is equal to plus 3.57 or you can write 3. Before solving it the number of digits in the decimal part of both the numbers should be same if not then put a 0 to make the number of digits in the decimal part same. Now we have 3.1 then we have written as 3.10, 12.56 so here we have made in the decimal part same by putting a 0 in the decimal part of 3.1. Now we can easily add this on the addition it will give plus 7.66. In the same way we can solve this example also which will give us the result as minus 8 point. Now consider the more example based on the addition and subtraction of fractions. Now where it is given initially this tank was 3 by 8 full. The tank was open and the tank is it means we have to find the increase. The increase will be equal to the difference of these two portions. So the increase is equal to 5 by 6 minus 3 by 8. Now these two are unlike fractions and we know how to subtract them now here and same of the denominators is so we have converted these two unlike fractions into like fractions and now increase is equal to 20 by 24 minus 9 by 24 which is equal to 20 minus 9 which is 11 upon 24. So this increase is equal to 11 by 24. Then we have learnt addition and subtraction of rational numbers and this completes our session hope you all have enjoyed the session.