Question

2 3/4 −(−1 1/2 )+(−5/6 )−(−3/8 )−(+4 2/3)

Answer 1

`2(3)/(4)-\left(-1(1)/(2)\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4(2)/(3)\right)=-(7)/(8)`

Explanation:

Given the expression

`2(3)/(4)-\left(-1(1)/(2)\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4(2)/(3)\right)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2(3)/(4)=(11)/(4)`

`(11)/(4)-\left(-1(1)/(2)\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4(2)/(3)\right)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 1(1)/(2)=(3)/(2)`

`(11)/(4)-\left(-(3)/(2)\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4(2)/(3)\right)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4(2)/(3)=(14)/(3)`

`(11)/(4)-\left(-(3)/(2)\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+(14)/(3)\right)`

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

`=(11)/(4)+(3)/(2)-(5)/(6)+(3)/(8)-(14)/(3)`

`\mathrm{Least\:Common\:Multiplier\:of\:}4,\:2,\:6,\:8,\:3:\quad 24`

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

`=(66)/(24)+(36)/(24)-(20)/(24)+(9)/(24)-(112)/(24)`

`\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)`

`=(66+36-20+9-112)/(24)`

`\mathrm{Add/Subtract\:the\:numbers:}\:66+36-20+9-112=-21`

`=(-21)/(24)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)`

`=-(21)/(24)`

`=-(7)/(8)`

Therefore,

`2(3)/(4)-\left(-1(1)/(2)\right)+\left(-5/6\right)-\left(-3/8\right)-\left(+4(2)/(3)\right)=-(7)/(8)`