simplify- 4/8 + 6/24 - 12/4 + 9/12 (13/9x-15/2) - (7/3x8/5) + (3/5x1/2)

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Solution

Taking the given expression as $\frac{4}{8} + \frac{6}{24} - \frac{12}{4} + \frac{9}{12} (\frac{13}{9} \times \frac{- 15}{2}) - (\frac{7}{3} \times \frac{8}{5}) + (\frac{3}{5} \times \frac{1}{2})$ ;
$\frac{4}{8} + \frac{6}{24} - \frac{12}{4} + \frac{9}{12} (\frac{13}{9} \times \frac{- 15}{2}) - (\frac{7}{3} \times \frac{8}{5}) + (\frac{3}{5} \times \frac{1}{2}) = \frac{1}{2} + \frac{1}{4} - 3 + \frac{3}{4} \times \frac{13}{3} \times \frac{- 5}{2} - \frac{56}{15} + \frac{3}{10} = \frac{1}{2} + \frac{1}{4} - 3 - \frac{195}{24} - \frac{56}{15} + \frac{3}{10} = \frac{2 + 1}{4} - (3 + \frac{195}{24} + \frac{56}{15}) + \frac{3}{10} = \frac{3}{4} - (\frac{360 + 975 + 448}{120}) + \frac{3}{10} = \frac{3}{4} - \frac{1783}{120} + \frac{3}{10} = \frac{450 - 8915 + 180}{600} = \frac{- 8285}{600} = \frac{- 1657}{120}$

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Similar questions

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

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

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

source $(i) \frac{8}{9} + \frac{- 11}{6} (i i) 3 + \frac{5}{- 7} (i i i) \frac{1}{- 12} a n d \frac{2}{- 15} (i v) \frac{- 8}{19} + \frac{- 4}{57} (v) \frac{7}{9} + \frac{3}{- 4} (v i) \frac{5}{26} + \frac{11}{- 39} (v i i) \frac{- 16}{9} + \frac{- 5}{12} (v i i i) \frac{- 13}{8} + \frac{5}{36} (i x) 0 + \frac{- 3}{5} (x) 1 + \frac{- 4}{5} (x i) \frac{- 5}{16} + \frac{7}{24}$

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$