Answer:
[tex]2\frac{3}{4}-\left(-1\frac{1}{2}\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4\frac{2}{3}\right)=-\frac{7}{8}[/tex]
Step-by-step explanation:
Given the expression
[tex]2\frac{3}{4}-\left(-1\frac{1}{2}\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4\frac{2}{3}\right)[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{3}{4}=\frac{11}{4}[/tex]
[tex]\frac{11}{4}-\left(-1\frac{1}{2}\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4\frac{2}{3}\right)[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 1\frac{1}{2}=\frac{3}{2}[/tex]
[tex]\frac{11}{4}-\left(-\frac{3}{2}\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4\frac{2}{3}\right)[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{2}{3}=\frac{14}{3}[/tex]
[tex]\frac{11}{4}-\left(-\frac{3}{2}\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+\frac{14}{3}\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a,\:-\left(-a\right)=a[/tex]
[tex]=\frac{11}{4}+\frac{3}{2}-\frac{5}{6}+\frac{3}{8}-\frac{14}{3}[/tex]
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}4,\:2,\:6,\:8,\:3:\quad 24[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]
[tex]=\frac{66}{24}+\frac{36}{24}-\frac{20}{24}+\frac{9}{24}-\frac{112}{24}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{66+36-20+9-112}{24}[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:66+36-20+9-112=-21[/tex]
[tex]=\frac{-21}{24}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{21}{24}[/tex]
[tex]=-\frac{7}{8}[/tex]
Therefore,
[tex]2\frac{3}{4}-\left(-1\frac{1}{2}\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4\frac{2}{3}\right)=-\frac{7}{8}[/tex]
