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
$\displaystyle 8\frac{5}{6} + 5\frac{2}{3} - 17\frac{7}{15} \\=8+\dfrac{5}{6} + 5+\dfrac{2}{3} - \color{#D61F06}{\{ 17+\dfrac{7}{15}\} }=\{ 8+5-17 \} +\{ \dfrac{5}{6} + \dfrac{2}{3} \color{#D61F06}{-} \dfrac{7}{15}\} \\ =-4 + \{ \dfrac{25}{30} + \dfrac{20}{30} - \dfrac{14}{30}\}~~~\because~the~ Lowest~ Common ~Multiple~is~~30\\=-4 + \dfrac{31}{30}=-5+1 \dfrac{1}{30} =-4+1+\dfrac{1}{30}=-3+\dfrac{1}{30}\\=\color{#D61F06}{-2+\{-1+\dfrac{1}{30} \} }=-2\dfrac{29}{30}~~\\Note~how ~we~ borrowed~-1~from~~- 3~~to~add~\dfrac{29}{30}~~$

#Algebra

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Toni Mackenzie - 5 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$