You can let your calculator figure this for you (see the attachment), or you can convert the numbers to improper fractions and divide in the usual way. (The "usual way" is to multiply the numerator fraction by the reciprocal of the denominator fraction.)
[tex]3\frac{3}{4}=3\cdot\dfrac{4}{4}+\dfrac{3}{4}=\dfrac{12+3}{4}=\dfrac{15}{4}\\\\-4\frac{2}{3}=-\left(4\cdot\dfrac{3}{3}+\dfrac{2}{3}\right)=-\left(\dfrac{12+2}{3}\right)=-\dfrac{14}{3}\\\\\text{Performing the division, we have ...}\\\displaystyle\frac{\left(\frac{15}{4}\right)}{\left(-\frac{14}{3}\right)}=\frac{15}{4}\times\frac{-3}{14}\\\\=-\frac{15\cdot 3}{4\cdot 14}\\\\=-\frac{45}{56}[/tex]
The quotient is -45/56.
