let's firstly convert the mixed fractions to improper fractions and then divide them.
[tex]\stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} ~\hfill \stackrel{mixed}{1\frac{5}{9}}\implies \cfrac{1\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{14}{9}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{14}{3}\div\cfrac{14}{9}\implies -\cfrac{~~\begin{matrix} 14 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{3}\cdot \cfrac{9}{~~\begin{matrix} 14 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{9}{3}\implies -3[/tex]
Answer:
-3
Step-by-step explanation:
Lets convert 4 2/3 to an improper fraction
-(4 * 3/3 + 2/3)/1 5/9
Combine 4 and 3/3
-(4 * 3/3 + 2/3)/1 5/9
Combine numerator over denom
-4 * 3 + 2/3/1 5/9
Simplify numerator
-12 + 2/3/1 5/9
Add 12 and 2
-14/3/1 5/9
Now we convert 1 5/9 to an improper.
-14/3/(9/9) + (5/9)
Combine
-14/3/(9 + 5)/9
Add 9 and 5
-14/3/(14/9)
Multiply yhe numerator by the reciprocal of the denom
-14/3 * 9/14
14(-1)/3 * 9/14
-1/3 * 9
Cancel the common factor of 3
-1/3 * (3(3))
-1 * 3 = -3
