 Hello and welcome to the session. In this session we will discuss a question which says that Find the sum of difference and write in simplest form first part minus 5 and 7 by 9 minus 2 and 4 by 9 plus 1 and 8 by 9 second part minus 4 and 3 by 8 plus 10 and 5 by 12 and third part is 1.08 plus absolute value of minus 16.20 minus of minus 3 now let us start with the solution of the given question now in the first part we have to simplify minus 5 and 7 by 9 minus 2 and 4 by 9 plus 1 and 8 by 9 now first of all we will convert these mixed fractions into improper fractions so this is equal to minus now 9 into 5 is 45 35 plus 7 is 52 so this is 52 by 9 that is minus 52 by 9 minus 9 into 2 is 18 18 plus 4 is 22 so this is 22 by 9 plus now 9 into 1 is 9 and 9 plus 8 is 17 so this is 17 by 9 now all these fractions have same denominator so we can take 9 as denominator now here we have 9 in the denominator and in the numerator we will have minus 52 minus 22 plus 17 now here first of all we will solve minus 52 and minus 22 now they have same sign that is minus so we will add the two numbers so this is equal to minus 74 plus 17 whole upon 9 now we will solve minus 74 plus 17 now here you can see one number is negative the other is positive so here we have to subtract these two numbers and in the answer we will put the sign of the greater number now here 74 is greater than 17 and 74 has minus sign so in the answer we will put minus sign so on subtracting this is equal to minus 57 upon 9 now 3 into 3 is 9 and 3 into 19 is 57 so this is equal to minus 19 upon 3 now in the mixed fraction it can be written as minus 6 and 1 upon 3 now let us start with the second part in which we have to simplify minus 4 and 3 by 8 plus 10 and 5 by 12 now again we will convert these mixed fractions into intact fractions so this will be equal to minus 35 upon 8 plus 125 upon 12 now these are unlike fractions that is the fractions with different denominators so let us convert these unlike fractions into like fractions that is the fractions with same denominators now lcm of the denominators that is lcm of 8 24 that is 3 into 2 into 2 into 2 which is equal to 24 now 8 into 3 is 25 and 12 into 2 is 24 so the fraction minus 35 by 8 can be written as minus 35 into 3 upon 8 into 3 which is equal to minus 105 upon 24 and the other fraction that is 125 upon 12 can be written as 125 into 2 upon 12 into 2 which is equal to upon 24 so we have converted the unlike fractions into like fractions that is the fractions with same denominators now minus 35 by 8 plus 125 by 12 will be equal to minus 105 by 25 plus 250 by 24 so this is equal to minus 105 plus 250 by 24 now here in the numerator one number is negative other is positive so we have to subtract and in the answer we will have the positive sign that is the sign with the greater number so subtracting we get 145 upon 24 and in the mixed fraction this can be written as 6 and 1 by 24 now let us start with the third part which is 1.08 plus the absolute value of minus 16.20 minus of minus 3 now we know that absolute value is always positive so we have the absolute value of minus a is equal to a that is the absolute value of any number minus a is equal to a so this is equal to 1.08 plus now we have absolute value of minus 16.20 will be 16.20 and here minus into minus will be plus 3 now here you can see in these numbers that is in the first two numbers in the decimal part we have two digits so here we will put two zeros in the decimal part of 3 so this will be 1.08 plus 16.20 plus 3.00 now we will add these three numbers and for adding the unit place digit should be written below the units place digit so adding these three numbers we get this equal to 20.20 so adding we get this equal to 20.20 so this is the solution of the given question and that's all for this session hope you all have enjoyed the session