Question

# Simplify: (1) $\frac{5}{9}+\frac{8}{9}$ (2) $\frac{13}{8}-\frac{7}{8}$ (3) $\frac{4}{5}+\frac{-7}{10}$ (4) $\frac{-10}{7}-\frac{1}{2}$ (5) $\frac{-13}{4}+\frac{-3}{4}$ (6) $\frac{-13}{4}-\frac{-3}{4}$ (7) $\frac{2}{5}-\frac{7}{9}$ (8) $\frac{-3}{5}+\frac{2}{7}$

Solution

## (1) $\frac{5}{9}+\frac{8}{9}$ $=\frac{5+8}{9}\phantom{\rule{0ex}{0ex}}=\frac{13}{9}$ (2) $\frac{13}{8}-\frac{7}{8}$ $=\frac{13-7}{8}\phantom{\rule{0ex}{0ex}}=\frac{6}{8}\phantom{\rule{0ex}{0ex}}=\frac{3}{4}$ (3) $\frac{4}{5}+\frac{-7}{10}$ $=\frac{4×2}{5×2}+\frac{-7}{10}\phantom{\rule{0ex}{0ex}}=\frac{8}{10}+\frac{-7}{10}\phantom{\rule{0ex}{0ex}}=\frac{8+\left(-7\right)}{10}\phantom{\rule{0ex}{0ex}}=\frac{8-7}{10}\phantom{\rule{0ex}{0ex}}=\frac{1}{10}$ (4) $\frac{-10}{7}-\frac{1}{2}$ $=\frac{\left(-10\right)×2}{7×2}-\frac{1×7}{2×7}\phantom{\rule{0ex}{0ex}}=\frac{-20}{14}-\frac{7}{14}\phantom{\rule{0ex}{0ex}}=\frac{-20-7}{14}\phantom{\rule{0ex}{0ex}}=\frac{-27}{14}$ (5) $\frac{-13}{4}+\frac{-3}{4}$ $=\frac{-13+\left(-3\right)}{4}\phantom{\rule{0ex}{0ex}}=\frac{-13-3}{4}\phantom{\rule{0ex}{0ex}}=\frac{-16}{4}\phantom{\rule{0ex}{0ex}}=-4$ (6) $\frac{-13}{4}-\frac{-3}{4}$ $=\frac{-13-\left(-3\right)}{4}\phantom{\rule{0ex}{0ex}}=\frac{-13+3}{4}\phantom{\rule{0ex}{0ex}}=\frac{-10}{4}\phantom{\rule{0ex}{0ex}}=\frac{-5}{2}$ (7) $\frac{2}{5}-\frac{7}{9}$ $=\frac{2×9}{5×9}-\frac{7×5}{9×5}\phantom{\rule{0ex}{0ex}}=\frac{18}{45}-\frac{35}{45}\phantom{\rule{0ex}{0ex}}=\frac{18-35}{45}\phantom{\rule{0ex}{0ex}}=\frac{-17}{45}$ (8) $\frac{-3}{5}+\frac{2}{7}$ $=\frac{-3×7}{5×7}+\frac{2×5}{7×5}\phantom{\rule{0ex}{0ex}}=\frac{-21}{35}+\frac{10}{35}\phantom{\rule{0ex}{0ex}}=\frac{-21+10}{35}\phantom{\rule{0ex}{0ex}}=\frac{-11}{35}$MathematicsMathematicsStandard VII

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