Question

3. Verify the following:

$( \frac{ 3}{8} + \frac{ { - 2}^{} }{3}) + \frac{ - 7}{12 =} = \frac{3}{8} + ( \frac{ - 2}{3} + \frac{ - 7}{12}$
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Answer 1

Answer :-

We have to show that :-

$\sf \left( \dfrac{ 3}{8} + \dfrac{ - 2}{ \: \: \: 3} \right) + \dfrac{ - 7}{ \: 12 } = \dfrac{3}{8} + \left( \dfrac{ - 2}{ \: \: \: 3} + \dfrac{ - 7}{ \: 12} \right)$

LHS

$\longmapsto\tt \left(\dfrac{3}{8} + \dfrac{ - 2}{ \: \: \: 3} \right) + \dfrac{ - 7}{12}$

$\longmapsto\tt \left(\dfrac{(3 \times 3) + (- 2 \times 8)}{24} \right) + \dfrac{ - 7}{12}$

$\longmapsto \tt\dfrac{9 - 16}{24} + \dfrac{ - 7}{12}$

$\longmapsto\tt \dfrac{ - 7}{24} + \dfrac{ - 7}{12}$

$\longmapsto \tt \dfrac{( - 7 \times 1) + ( - 7 \times 2)}{24}$

$\longmapsto\tt \dfrac{ - 7 - 14}{24}$

$\longmapsto \tt\dfrac{ - 21}{ \: \: \: 24}$

$\longmapsto \tt \dfrac{ - 7}{ \: \: \: 8}$

RHS

$\longmapsto\tt \dfrac{3}{8} + \left( \dfrac{ - 2}{ \: \: \: 3} + \dfrac{ - 7}{12} \right)$

$\longmapsto\tt\dfrac{3}{8} + \left( \dfrac{( - 2 \times4) + ( - 7 \times 1)}{12} \right)$

$\longmapsto\tt \dfrac{3}{8} + \dfrac{ - 8 - 7}{12}$

$\longmapsto\tt\dfrac{3}{8} + \dfrac{ - 15}{ \: \: \: 12}$

$\longmapsto\tt \dfrac{(3 \times 3) + ( - 15 \times 2)}{24}$

$\longmapsto\tt \dfrac{9 - 30}{24}$

$\longmapsto\tt\dfrac{ - 21}{ \: \: 24}$

$\longmapsto\tt\dfrac{ - 7}{ \: \: 8}$

LHS = RHS.

Hence verified!