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} $

To do:

We have to simplify the given expressions.

Solution:

(i) \( \frac{-3}{2}+\frac{5}{4}-\frac{7}{4} \)

LCM of $2$ and $4=4$

$\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}= \frac{(-3)(2)+(5)(1)-(7)(1)}{4}$

$= \frac{-6+5-7}{4}$

$=\frac{-8}{4}$

$=-2$

Therefore,

$\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}=-2$.      

(ii) \( \frac{5}{3}-\frac{7}{6}+\frac{-2}{3} \)

LCM of $3$ and $6=6$

$\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}= \frac{(5)(2)-(7)(1)+(-2)(2)}{6}$

$= \frac{10-7-4}{6}$

$=\frac{-1}{6}$

Therefore,

$\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}=\frac{-1}{6}$.       

(iii) \( \frac{5}{4}-\frac{7}{6}-\frac{-2}{3} \)

LCM of $3,4$ and $6=12$

$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}= \frac{(5)(3)-(7)(2)-(-2)(4)}{12}$

$= \frac{15-14+8}{12}$

$=\frac{9}{12}$

$=\frac{3}{4}$

Therefore,

$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\frac{3}{4}$.        

(iv) \( \frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7} \)

LCM of $5,7$ and $10=70$

$\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}= \frac{(-2)(14)-(-3)(7)-(-4)(10)}{70}$

$= \frac{-28+21+40}{70}$

$=\frac{33}{70}$

Therefore,

$\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}=\frac{33}{70}$.

(v) \( \frac{5}{6}+\frac{-2}{5}-\frac{-2}{15} \)

LCM of $6,5$ and $15=30$

$\frac{5}{6}+\frac{-2}{5}-\frac{-2}{15}= \frac{(5)(5)+(-2)(6)-(-2)(2)}{30}$

$= \frac{25-12+4}{30}$

$=\frac{17}{30}$

Therefore,

$\frac{5}{6}+\frac{-2}{5}-\frac{-2}{15}=\frac{17}{30}$. 

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

LCM of $8,9$ and $36=72$

$\frac{3}{8}-\frac{-2}{9}+\frac{-5}{36}= \frac{(3)(9)-(-2)(8)+(-5)(2)}{72}$

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

$=\frac{33}{72}$

$=\frac{11}{24}$

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Updated on: 10-Oct-2022

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