question_answer 1)

Find the sum: (i) \[\frac{5}{4}+\left( \frac{-11}{4} \right)\]                         (ii) \[\frac{5}{3}+\frac{3}{5}\]                      (iii) \[\frac{-9}{10}+\frac{22}{15}\]                    (iv) \[\frac{-3}{-11}+\frac{5}{9}\] (v) \[\frac{-8}{19}+\frac{(-2)}{57}\]                          (v) \[\frac{-8}{19}+\frac{(-2)}{57}\]                          (vi) \[\frac{-2}{3}+0\]                              (vii) \[-2\frac{1}{3}+4\frac{3}{5}\]

Answer:

                (i) \[\frac{5}{4}+\frac{(-11)}{4}=\frac{5+(-11)}{4}=\frac{-6}{4}=\frac{-6\div 2}{4\div 2}=\frac{-3}{2}\]                 (ii) LCM of 3 and 5 is 15.                 So, \[\frac{5}{3}=\frac{25}{15}\] and  \[\frac{3}{5}=\frac{9}{15}\]                 Thus, \[\frac{5}{3}+\frac{3}{5}=\frac{25}{15}+\frac{9}{15}=\frac{25+9}{15}=\frac{34}{15}=2\frac{4}{15}\].                 (iii) LCM of 10 and 15 is 30.                 So, \[\frac{-9}{10}=\frac{-27}{30}\] and  \[\frac{22}{15}=\frac{44}{30}\]                 Thus, \[\frac{-9}{10}+\frac{22}{15}=\frac{-27}{30}+\frac{44}{30}=\frac{-27+44}{30}=\frac{17}{30}\]                 (iv) LCM of 11 and 9 is 99.                 \[\frac{-3}{-11}=\frac{3}{11},\frac{3}{11}=\frac{27}{99},\frac{5}{9}=\frac{55}{99}\]                 Thus, \[\frac{3}{11}+\frac{5}{9}=\frac{27}{99}+\frac{55}{99}=\frac{27+55}{99}=\frac{82}{99}\]                 (v) LCM of 19 and 57 is 57.                 \[\frac{-8}{19}=\frac{-24}{57},\frac{-2}{57}=\frac{-2}{57}\] Thus, \[\frac{-8}{19}+\frac{(-2)}{57}=\frac{-24}{57}+\frac{(-2)}{57}=\frac{(-24)+(-2)}{57}=\frac{-26}{57}\]                 (vi) \[\frac{-2}{3}+0=\frac{-2}{3}\]                 (vii) LCM of 3 and 5 is 15.                 \[-2\frac{1}{3}+4\frac{3}{5}=-\frac{7}{3}+\frac{23}{5}\]                 \[\frac{-7}{3}=\frac{-35}{15},\frac{23}{5}=\frac{69}{15}\]                 Thus, \[\frac{-7}{3}+\frac{23}{5}=\frac{-35}{15}+\frac{69}{15}=\frac{-35+69}{15}=\frac{34}{15}\].