Question

$\frac{ - 2}{3} - \frac{5}{6}$
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Answer 1

Answer:

$\dfrac{-2}{3}-\dfrac{5}{6}=-\dfrac{3}{2}\quad \left(\mathrm{Decimal:\quad }\:-1.5\right)$

Step-by-step explanation:

$\dfrac{-2}{3}-\dfrac{5}{6}$

$\gray{\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{-a}{b}=-\dfrac{a}{b}}$

$=-\dfrac{2}{3}-\dfrac{5}{6}$

$\black{\mathrm{Least\:Common\:Multiplier\:of\:}3,\:6:\quad 6}$

$\black{\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}}$

$\gray{\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}}$ $\gray{\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:6}$

$\gray{\mathrm{For}\:\dfrac{2}{3}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:2}$

$\dfrac{2}{3}=\dfrac{2\cdot \:2}{3\cdot \:2}=\dfrac{4}{6}$

$=-\dfrac{4}{6}-\dfrac{5}{6}$

$\gray{\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \dfrac{a}{c}\pm \dfrac{b}{c}=\dfrac{a\pm \:b}{c}}$

$=\dfrac{-4-5}{6}$

$\gray{\mathrm{Subtract\:the\:numbers:}\:-4-5=-9}$

$=\dfrac{-9}{6}$

$\gray{\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{-a}{b}=-\dfrac{a}{b}}$

$=-\dfrac{9}{6}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:3}$

$=-\dfrac{3}{2}$