

InterviewSolution
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Simplify:(i) \((\frac{25}{8}\times \frac{2}{5})-(\frac{3}{5}\times \frac{-10}{9})\)(ii) \((\frac{1}{2}\times \frac{1}{4})+(\frac{1}{2}\times 6)\)(iii) \((-5\times \frac{2}{15})-(-6\times \frac{2}{9})\)(iv) \((\frac{-9}{4}\times \frac{5}{3})+(\frac{13}{2}\times \frac{5}{6})\)(v) \((\frac{-4}{3}\times \frac{12}{-5})+(\frac{3}{7}\times \frac{21}{15})\)(vi) \((\frac{13}{5}\times \frac{8}{3})-(\frac{-5}{2}\times \frac{11}{3})\)(vii) \((\frac{13}{7}\times \frac{11}{26})-(\frac{-4}{3}\times \frac{5}{6})\)(viii) \((\frac{8}{5}\times \frac{-3}{2})+(\frac{-3}{10}\times \frac{11}{16})\) |
Answer» (i) \(\frac{25\times 2}{8\times 5}-\frac{3\times -10}{5\times 9}\) = \(\frac{50}{40}+\frac{30}{45}\) = \(\frac{5}{4}+\frac{2}{3}\) = \(\frac{15+8}{12}\) = \(\frac{23}{12}\) (ii) \(\frac{1\times 1}{2\times 4}+\frac{1\times 6}{2\times 1}\) = \(\frac{1}{8}+\frac{6}{2}\) = \(\frac{1}{8}+3\) = \(\frac{1+24}{8}\) = \(\frac{25}{8}\) (iii) \(\frac{-5\times 2}{1\times 15}+\frac{6\times 2}{1\times 9}\) = \(\frac{-10}{15}+\frac{12}{9}\) = \(\frac{-2}{3}+\frac{4}{3}\) = \(\frac{-2+4}{3}\) = \(\frac{2}{3}\) (iv) \(\frac{-9\times 5}{4\times 3}+\frac{13\times 5}{2\times 6}\) = \(\frac{-45}{12}+\frac{65}{12}\) = \(\frac{-45+65}{12}\) = \(\frac{20}{12}\) = \(\frac{5}{3}\) (v) \(\frac{-4\times 12}{3\times -5}+\frac{3\times 21}{7\times 15}\) = \(\frac{4\times 4}{1\times 5}+\frac{1\times 3}{1\times 5}\) = \(\frac{16}{5}+\frac{3}{5}\) = \(\frac{19}{5}\) (vi) \(\frac{13\times 8}{5\times 3}+\frac{5\times 11}{2\times 3}\) = \(\frac{104}{15}+\frac{15}{6}\) = \(\frac{104\times 2+55\times 6}{30}\) = \(\frac{483}{30}\) (vii) \(\frac{13\times 11}{7\times 26}+\frac{4\times 5}{3\times 6}\) = \(\frac{1\times 11}{7\times 2}+\frac{4\times 5}{3\times 6}\) = \(\frac{11}{14}+\frac{20}{18}\) = \(\frac{11\times 9+20\times 7}{126}\) = \(\frac{99+140}{126}\) = \(\frac{239}{126}\) (viii) \(\frac{8\times -3}{5\times 2}-\frac{3\times 11}{10\times 16}\) = \(\frac{-24}{10}-\frac{33}{160}\) = \(\frac{-24\times 16-33\times 1}{160}\) = \(\frac{-384-33}{160}\) = \(\frac{-417}{160}\) |
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