Rearrange suitably and find the sum in each of the following:

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

Open in App

Solution

Given $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

$∴$ $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$
$= \frac{- 5}{8} + (\frac{4}{13} + \frac{- 8}{13} + \frac{9}{13})$
$= \frac{- 5}{8} + (\frac{4 - 8 + 9}{13})$
$= \frac{- 5}{8} + (\frac{5}{13})$
$= \frac{- 5 \times 13}{8 \times 13} + \frac{5 \times 8}{13 \times 8}$
$= \frac{- 65}{104} + \frac{40}{104}$
$= \frac{- 25}{104}$

Hence, $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13} = \frac{- 25}{104}$

Suggest Corrections

Similar questions

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

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}

\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}

\frac{4}{7} + (\frac{- 4}{9}) + \frac{3}{7} + (\frac{- 13}{9})

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program