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# Add and subtract Mix fractions

When adding (or subtracting) mix fractions, it would be simpler to split the whole numbers and proper fractions. Solve the whole numbers and fractions separately. Then combine the two for the final result. Say
$$\displaystyle 8\frac{5}{6} + 5\frac{2}{3} - 17\frac{7}{15} \\=8+\dfrac{5}{6} + 5+\dfrac{2}{3} - \color{red}{\{ 17+\dfrac{7}{15}\} }=\{ 8+5-17 \} +\{ \dfrac{5}{6} + \dfrac{2}{3} \color{red}{-} \dfrac{7}{15}\} \\ =-4 + \{ \dfrac{25}{30} + \dfrac{20}{30} - \dfrac{14}{30}\}~~~\because~the~ Lowest~ Common ~Multiple~is~~30\\=-4 + \dfrac{31}{30}=-5+1 \dfrac{1}{30} =-4+1+\dfrac{1}{30}=-3+\dfrac{1}{30}\\=\color{red}{-2+\{-1+\dfrac{1}{30} \} }=-2\dfrac{29}{30}~~\\Note~how ~we~ borrowed~-1~from~~- 3~~to~add~\dfrac{29}{30}~~$$

Note by Niranjan Khanderia
2 years, 3 months ago

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