Question

Question:

$\frac{2}{3} - ( \frac{4}{5} - \frac{5}{6} ) \: and \: (\frac{2}{3} - \frac{4}{5} ) - \frac{5}{6} . \: \: \: \: \: \\ are \: the \: 2 \: sums \: equal?$
Chapter Rational Numbers!
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Answer 1

Answer

tex] \frac{2}{3} - ( \frac{4}{5} - \frac{5}{6} ) \: and \: (\frac{2}{3} - \frac{4}{5} ) - \frac{5}{6} . \: \: \: \: \: \\ are \: the \: 2 \: sums \: equal? [/tex]

Hope the above answer is helpful

Answer 2

$\large \underline{ \frak{Given:-}}$

$\red{ \sf{ \frac{2}{3} - ( \frac{4}{5} - \frac{5}{6} ) \: and \: (\frac{2}{3} - \frac{4}{5} ) - \frac{5}{6}}}$

$\large \underline{ \frak{To \: find{:-}}}$

Whether these two sums are equal.

$\large \underline{ \frak{Solution{:-}}}$

$\underline{ \rm{Given \: Equation{:-}}}$

${ \rm{ \frac{2}{3} - ( \frac{4}{5} - \frac{5}{6} ) \: and \: (\frac{2}{3} - \frac{4}{5} ) - \frac{5}{6}}}$

(♪ First we have to solve the L.H.S.

So,

$\frac{2}{3} - \frac{24 - 25}{30}$

$\frac{2}{3} - ( \frac{ - 1}{30} )$

$\star\displaystyle {\purple{\boxed {\bf\frac{ - 7}{10} }}}$

Now,

(♪ we have to solve the R.H.S.

So,

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

$\frac{ - 2}{15} - \frac{5}{6}$

$\star \displaystyle {\orange{\boxed {\bf \frac{ - 29}{30} }}}$

Therefore,

$\large\boxed{ \frak{L.H.S ≠ R.H.S}}$

$\qquad{ \rule{250pt}{2.9pt}}$