question_answer 1)

Find: (i) \[\frac{7}{24}-\frac{17}{36}\]                 (ii) \[\frac{5}{63}-\left( \frac{-6}{21} \right)\]                       (iii) \[\frac{-6}{13}-\left( \frac{-7}{15} \right)\]                            (iv) \[\frac{-3}{8}-\frac{7}{11}\] (v) \[-2\frac{1}{9}-6\]

Answer:

                (i) \[\frac{7}{24}-\frac{17}{36}=\frac{7}{24}+\frac{(-17)}{36}\] LCM of 24 and 36 is 72. \[\frac{7}{24}=\frac{21}{72},\frac{(-17)}{36}=\frac{(-34)}{72}\] Thus, \[\frac{7}{24}+\frac{(-17)}{36}=\frac{21}{72}+\frac{(-34)}{72}=\frac{21+(-34)}{72}=\frac{-13}{72}\] (ii) \[\frac{5}{63}-\left( -\frac{6}{21} \right)=\frac{5}{63}+\frac{6}{21}\] LCM of 63 and 21 is 63 \[\frac{6}{21}=\frac{18}{63}\] Thus, \[\frac{5}{63}+\frac{6}{21}=\frac{5}{63}+\frac{18}{63}=\frac{5+18}{63}=\frac{23}{63}\] (iii) \[\frac{-6}{13}-\left( \frac{-7}{15} \right)=\frac{-6}{13}+\frac{7}{15}\] LCM of 13 and 15 is 195 \[\frac{-6}{13}=\frac{-90}{195},\frac{7}{15}=\frac{91}{195}\] Thus, \[\frac{-6}{13}+\frac{7}{15}=\frac{-90}{195}+\frac{91}{195}=\frac{-90+91}{195}=\frac{1}{195}\].                 (iv) \[\frac{-3}{8}-\frac{7}{11}=\frac{-3}{8}+\left( \frac{-7}{11} \right)\] LCM of 8 and 11 is 88.                 \[\frac{-3}{8}=\frac{-33}{88},\frac{(-7)}{11}=\frac{(-56)}{88}\]                 Thus, \[\frac{-3}{8}+\frac{(-7)}{11}=\frac{-33}{88}+\frac{(-56)}{88}\] \[=\frac{-33+(-56)}{88}=\frac{-89}{88}=-1\frac{1}{88}\]  (v) \[-2\frac{1}{9}-6=\frac{-19}{9}-6=\frac{-19}{6}+(-6)=\frac{-19}{6}+\frac{(-6)}{1}\] LCM of 6 and 1 is 6. \[\frac{(-6)}{1}=\frac{(-36)}{6}\]                 Thus, \[\frac{-19}{6}+\frac{(-6)}{1}=\frac{(-19)}{6}+\frac{(-36)}{6}=\frac{-19+(-36)}{6}\]\[=\frac{-55}{6}=-9\frac{1}{6}\].