Simplify:
(i) $\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}$
(ii) $\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}$
(iii) $\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
(iv) $\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}$
(v) $\frac{5}{6}+\frac{-2}{5}-\frac{-2}{15}$
(vi) $\frac{3}{8}-\frac{-2}{9}+\frac{-5}{36}$
(i) \frac{-3}{2}+\frac{5}{4}-\frac{7}{4}
Taking the L.C.M. of the denominators:
$\frac{-6}{4}+\frac{5}{4}-\frac{7}{4}$
$=\frac{-6+5-7}{4}$
$=\frac{-8}{4}$
$=-2$
(ii) $\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}$
Taking the L.C.M. of the denominators :
$\frac{10}{6}-\frac{7}{6}+\frac{-4}{6}$
$=\frac{10-7+(-4)}{6}$
$=\frac{10-7-4}{6}$
$=\frac{-1}{6}$
(iii) $\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
Taking the L.C.M. of the denominators:
$\frac{15}{12}-\frac{14}{12}-\frac{-8}{12}$
$=\frac{15-14-(-8)}{12}$
$=\frac{15-14+8}{12}$
$=\frac{9}{12}$
$=\frac{3}{4}$
(iv) $\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}$
Taking the $L . C . M .$ of the denominators :
$\frac{-28}{70}-\frac{-21}{70}-\frac{-40}{70}$
$=\frac{(-28)-(-21)-(-40)}{70}$
$=\frac{-28+21+40}{70}$
$=\frac{33}{70}$
(v) $\frac{5}{6}+\frac{-2}{5}-\frac{-2}{15}$
Taking the L.C.M. of the denominators :
$\frac{25}{30}+\frac{-12}{30}-\frac{-4}{30}$
$=\frac{25+(-12)-(-4)}{30}$
$=\frac{25-12+4}{30}$
$=\frac{17}{30}$
(vi) $\frac{3}{8}-\frac{-2}{9}+\frac{-5}{36}$
Taking the L.C. $M$. of the denominators :
$\frac{27}{72}-\frac{-16}{72}+\frac{-10}{72}$
$=\frac{27-(-16)+(-10)}{72}$
$=\frac{27+16-10}{72}$
$=\frac{33}{72}$
$=\frac{11}{24}$
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