Question

3/5 × [-2/7] + [-2/3] + 3/4

Answer 1

Answer:

$\dfrac{3}{5}\left(-\dfrac{2}{7}\right)+\left(-\dfrac{2}{3}\right)+\dfrac{3}{4}=-\dfrac{37}{420}\quad \left(\mathrm{Decimal:\quad }\:-0.08810\dots \right)$

Step-by-step explanation:

$\dfrac{3}{5}\left(-\dfrac{2}{7}\right)+\left(-\dfrac{2}{3}\right)+\dfrac{3}{4}$

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

$=-\dfrac{3}{5}\times \dfrac{2}{7}-\dfrac{2}{3}+\dfrac{3}{4}$

$\dfrac{3}{5}\times \dfrac{2}{7}=\dfrac{6}{35}$

$=-\dfrac{6}{35}-\dfrac{2}{3}+\dfrac{3}{4}$

$\mathrm{Least\:Common\:Multiplier\:of\:}35,\:3,\:4$

$\mathrm{Prime\:factorization\:of\:}35:\quad 5\times \:7$

$\mathrm{Prime\:factorization\:of\:}3:\quad 3$

$\mathrm{Prime\:factorization\:of\:}4:\quad 2\times \:2$

$\mathrm{Compute\:a\:number\:comprised\:of\:factors\:that\:appear\:in\:at\:least\:one\:of\:the\:following:}$ $35,\:3,\:4$

$=5\times \:7\times \:3\times \:2\times \:2$

$\mathrm{Multiply\:the\:numbers:}\:5\times \:7\times \:3\times \:2\times \:2=420$

$=420$

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

$\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}$ $\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:420$

$\mathrm{For}\:\dfrac{6}{35}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:12$

$\dfrac{6}{35}=\dfrac{6\times \:12}{35\times \:12}=\dfrac{72}{420}$

$\mathrm{For}\:\dfrac{2}{3}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:140$

$\dfrac{2}{3}=\dfrac{2\times \:140}{3\times \:140}=\dfrac{280}{420}$

$\mathrm{For}\:\dfrac{3}{4}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:105$

$\dfrac{3}{4}=\dfrac{3\times \:105}{4\times \:105}=\dfrac{315}{420}$

$=-\dfrac{72}{420}-\dfrac{280}{420}+\dfrac{315}{420}$

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

$=\dfrac{-72-280+315}{420}$

$\mathrm{Add/Subtract\:the\:numbers:}\:-72-280+315=-37$

$=\dfrac{-37}{420}$

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

$=-\dfrac{37}{420}$