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Find using appropriate properties 1/5x -2/7-1/6x3/7+3/14x1/5

Dear student

We have, \frac{1}{5} \times (\frac{- 2}{7}) - \frac{1}{6} \times \frac{3}{7} + \frac{3}{14} \times \frac{1}{5} = \frac{1}{7} (\frac{- 2}{5} - \frac{3}{6} + \frac{3}{2 \times 5}) = \frac{1}{7} (\frac{- 2}{5} - \frac{1}{2} + \frac{3}{10}) = \frac{1}{7} (\frac{- 4 - 5 + 3}{10}) = \frac{1}{7} (\frac{- 9 + 3}{10}) = \frac{1}{7} (\frac{- 6}{10}) = \frac{1}{7} \times (\frac{- 3}{5}) = \frac{- 3}{35} Note : a (b + c + d) = ab + ac + ad

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