# Simplify:

Question:

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) $\frac{3}{8}-\frac{-2}{9}+\frac{-5}{36}$

Solution:

(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 :

$\frac{27}{72}-\frac{-16}{72}+\frac{-10}{72}$

$=\frac{27-(-16)+(-10)}{72}$

$=\frac{27+16-10}{72}$

$=\frac{33}{72}$

$=\frac{11}{24}$