Question

evaluate -5 + 5/-8+ -5/-12​

Answer 1

Answer:

$-5+\frac{5}{-8}-\frac{5}{-12}=-\frac{125}{24}\quad \left(\mathrm{Decimal:\quad }\:-5.20833\dots \right)$

Step-by-step explanation:

$-5+\frac{5}{-8}-\frac{5}{-12}$

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

$\gray{=-5-\frac{5}{8}-\frac{5}{-12}}$

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

$=-5-\frac{5}{8}-\left(-\frac{5}{12}\right)$

$\gray{\mathrm{Apply\:rule}\:-\left(-a\right)=a}$

$=-5-\frac{5}{8}+\frac{5}{12}$

$\gray{\mathrm{Convert\:element\:to\:fraction}:\quad \:5=\frac{5}{1}}$

$=-\frac{5}{1}-\frac{5}{8}+\frac{5}{12}$

$\black{\mathrm{Least\:Common\:Multiplier\:of\:}1,\:8,\:12:}$

$1,\:8,\:12$

$\gray{\mathrm{Prime\:factorization\:of\:}1}$

$\gray{\mathrm{Prime\:factorization\:of\:}8:\quad 2\cdot \:2\cdot \:2}$

$\gray{\mathrm{Prime\:factorization\:of\:}12:\quad 2\cdot \:2\cdot \:3}$

$\gray{\mathrm{Compute\:a\:number\:comprised\:of\:factors\:that\:appear\:in\:at\:least\:one\:of\:the\:following:}}$ $\gray{1,\:8,\:12}$

$=2\cdot \:2\cdot \:2\cdot \:3$

$\gray{\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2\cdot \:3=24}$

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

$\gray{\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}}$ $\gray{\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:24}$

$\gray{\mathrm{For}\:\frac{5}{1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:24}$

$\frac{5}{1}=\frac{5\cdot \:24}{1\cdot \:24}=\frac{120}{24}$

$\gray{\mathrm{For}\:\frac{5}{8}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:3}$

$\frac{5}{8}=\frac{5\cdot \:3}{8\cdot \:3}=\frac{15}{24}$

$\gray{\mathrm{For}\:\frac{5}{12}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:2}$

$\frac{5}{12}=\frac{5\cdot \:2}{12\cdot \:2}=\frac{10}{24}$

$=-\frac{120}{24}-\frac{15}{24}+\frac{10}{24}$

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

$=\frac{-120-15+10}{24}$

$\gray{\mathrm{Add/Subtract\:the\:numbers:}\:-120-15+10=-125}$

$=\frac{-125}{24}$

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

$=-\frac{125}{24}$