Given:
[tex]-\frac{2}{3}\text{ }\div\text{ 3}\frac{3}{4}[/tex]For us to be able to proceed, let's first convert the mixed number 3 and 3/4 into an improper fraction.
We get,
[tex]\text{ 3}\frac{3}{4}\text{ = }\frac{\text{ (3 x 4) + 3}}{\text{ 4}}\text{ = }\frac{\text{ 12 + 3}}{\text{ 4}}\text{ = }\frac{\text{ 15}}{\text{ 4}}[/tex]Therefore, the improper fraction equivalent of 3 and 3/4 is 15/4.
Let's now proceed in dividing fractions,
[tex]-\frac{2}{3}\text{ }\div\text{ 3}\frac{3}{4}\text{ = }-\frac{2}{3}\text{ }\div\text{ }\frac{\text{ 15}}{\text{ 4}}[/tex][tex]-\frac{2}{3}\text{ }\div\text{ }\frac{\text{ 15}}{\text{ 4}}\text{ = }-\frac{2}{3}\text{ x }\frac{\text{ 4}}{\text{ 15}}\text{ = -}\frac{\text{ 2 x 4}}{\text{ 3 x 15}}[/tex][tex]=\text{ -}\frac{\text{ 8}}{\text{ 45}}[/tex]We can no longer simplify -8/45.
Therefore, the answer is -8/45.
