Question

How do you simplify -3 1/9 - (-1 1/3)

Answer 1

`-3(1)/(9)-\left(-1(1)/(3)\right)\\`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions:}`

`3(1)/(9)\\=(28)/(9)\\=-(28)/(9)-\left(-1(1)/(3)\right)\\`

-

`=-(28)/(9)-\left(-(4)/(3)\right)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions:}`

`\mathrm{Apply\:rule}:\quad \:a-\left(-b\right)=a+b\\-(28)/(9)-\left(-(4)/(3)\right)=-(28)/(9)+(4)/(3)\\=-(28)/(9)+(4)/(3)`

`=-(28)/(9)+(12)/(9)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(c)+(b)/(c)=(a+b)/(c)\\=(-28+12)/(9)\\\mathrm{Add\:the\:numbers:}\:-28+12=-16\\=(-16)/(9)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)\\=-(16)/(9)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions:}`

`(16)/(9)=1(7)/(9)\\(16)/(9)=1 \\9\overline\smallspace16\:\:\:\:\\\begin{matrix}\:\:\:\:\:\:\emptyspace1\:\:\:\:\:\:\:\:\:\:\:\:\\ 9\overline\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace9}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\\\\\\(16)/(9)=1(7)/(9)\\=-1(7)/(9)\\answer: \\=-1(7)/(9)`