Question

if a=-11/27,b=4/9and c=-5/18,then verify that a+(b+c)=(a+b)+c​

Answer 1

a + (b + c) = (a + b) + c​

L.H.S. = a + (b + c)

          = $-\frac{11}{27}$ + ($\frac{4}{9}$ + $-\frac{5}{18}$)

          = $-\frac{11}{27}$ + ($\frac{8}{18}$ - $\frac{5}{18}$)

          = $-\frac{11}{27}$ + $\frac{3}{18}$

          = $-\frac{22}{54}$ + $\frac{9}{54}$

          = $-\frac{13}{54}$

R.H.S. = (a + b) + c​

          = ($-\frac{11}{27}$ + $\frac{4}{9}$) + $-\frac{5}{18}$

          = ($-\frac{11}{27}$ + $\frac{12}{27}$) + $-\frac{5}{18}$

          = $\frac{1}{27}$ + $-\frac{5}{18}$

          = $\frac{2}{54}$ - $\frac{15}{54}$

          = $-\frac{13}{54}$

∵ L.H.S. = R.H.S.

∴ a + (b + c) ≡ (a + b) + c​