Question

3/7 +(-16/11)+(-8/21)+(5/22)

Answer 1

Answer:

-551/462

Step-by-step explanation:

3/7+(-16/11)+(-8/21)+(5/22)

3/7-16/11-8/21+5/22

LCM= 462

66×3/462-42×16/462-22×8/462+21×5/462

192/462-672/462-176/462+105/462

-480-71/462

-551/462 ans.

Answer 2

Answer:

$\left(\dfrac{3}{7}\right)+\left(-\dfrac{16}{11}\right)+\left(-\dfrac{8}{21}\right)+\left(\dfrac{5}{22}\right)=-\dfrac{545}{462}\quad \left(\mathrm{Decimal:\quad }\:-1.17965\dots \right)$

Step-by-step explanation:

$\left(\dfrac{3}{7}\right)+\left(-\dfrac{16}{11}\right)+\left(-\dfrac{8}{21}\right)+\left(\dfrac{5}{22}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$=\dfrac{3}{7}-\dfrac{16}{11}-\dfrac{8}{21}+\dfrac{5}{22}$

$\mathrm{Least\:Common\:Multiplier\:of\:}7,\:11,\:21,\:22$

$\mathrm{Prime\:factorization\:of\:}7:\quad 7$

$\mathrm{Prime\:factorization\:of\:}11:\quad 11$

$\mathrm{Prime\:factorization\:of\:}21:\quad 3\cdot \:7$

$\mathrm{Prime\:factorization\:of\:}22:\quad 2\cdot \:11$

$\mathrm{Compute\:a\:number\:comprised\:of\:factors\:that\:appear\:in\:at\:least\:one\:of\:the\:following:}$ $7,\:11,\:21,\:22$

$=7\cdot \:11\cdot \:3\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:7\cdot \:11\cdot \:3\cdot \:2=462$

$=462$

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

$\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}$ $\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:462$

$\mathrm{For}\:\dfrac{3}{7}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:66$

$\dfrac{3}{7}=\dfrac{3\cdot \:66}{7\cdot \:66}=\dfrac{198}{462}$

$\mathrm{For}\:\dfrac{16}{11}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:42$

$\dfrac{16}{11}=\dfrac{16\cdot \:42}{11\cdot \:42}=\dfrac{672}{462}$

$\mathrm{For}\:\dfrac{8}{21}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:22$

$\dfrac{8}{21}=\dfrac{8\cdot \:22}{21\cdot \:22}=\dfrac{176}{462}$

$\mathrm{For}\:\dfrac{5}{22}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:21$

$\dfrac{5}{22}=\dfrac{5\cdot \:21}{22\cdot \:21}=\dfrac{105}{462}$

$=\dfrac{198}{462}-\dfrac{672}{462}-\dfrac{176}{462}+\dfrac{105}{462}$

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

$=\dfrac{198-672-176+105}{462}$

$\mathrm{Add/Subtract\:the\:numbers:}\:198-672-176+105=-545$

$=\dfrac{-545}{462}$

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

$=-\dfrac{545}{462}$