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Mathematics

Simplify: 212314+5562\dfrac{1}{2} - 3\dfrac{1}{4} + 5\dfrac{5}{6}

Fractions

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Answer

LCM of 2, 4 and 6 = 12.

52134+3565×62×613×34×3+35×26×230123912+70123039+701261125112\Rightarrow \dfrac{5}{2} - \dfrac{13}{4} + \dfrac{35}{6}\\[1em] \Rightarrow \dfrac{5 \times 6}{2 \times 6} - \dfrac{13 \times 3}{4 \times 3} + \dfrac{35 \times 2}{6 \times 2}\\[1em] \Rightarrow \dfrac{30}{12} - \dfrac{39}{12} + \dfrac{70}{12}\\[1em] \Rightarrow \dfrac{30 - 39 + 70}{12}\\[1em] \Rightarrow \dfrac{61}{12}\\[1em] \Rightarrow 5\dfrac{1}{12}

Hence, 212314+556=51122\dfrac{1}{2} - 3\dfrac{1}{4} + 5\dfrac{5}{6} = 5\dfrac{1}{12}.

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