Adding Rational Numbers

Adding Rational Numbers A number of the form p / q, where p and q are integers prime to each other and q 0, is called a rational number or commensurable quantity; here q is taken as a positive integer and p may be a positive integer or negative integer or zero. For example, each of the numbers 5, 2/3, 0.32, 16 etc. is a rational number. Evidently, the number 0 (zero) is a rational number. Adding rational numbers: - Suppose there are two rational numbers a / b and c / d. Then a/ b + c/ d= (a d + b c) / b d Where b 0 and d 0 Example of adding ration numbers: - Simplify 1 / 2 + 3 / 4 Solution: - 1 / 2 + 3 / 4 = (1 * 3 + 2 * 4)/ (2 * 4) = (3 + 8) / 8 = 11 / 8 Simplify the following expression:- 1/ 5 + 2/ 15 + 3/ 10 Solution: - At first we will take the least common factor of the denominators 5, 15 and 10. L.C.M. of 5, 15 and 10 = 30 Now we will divide 30 by each denominator 5, 15 and 10 then multiply with there corresponding numerators. Like 30 / 5 = 6 and 1* 6= 6 Similarly we will proceed for the next two rational numbers. 1/ 5 + 2/ 15 + 3/ 10= (1*6 + 2* 2 + 3* 3) / 30 = (6+4+9)/30 = 19 / 30