To solve the division of these fractions, we follow a step-by-step process:
1. Understand the operation: Division by a fraction is the same as multiplying by its reciprocal. Therefore, we need to take the reciprocal of [tex]\(-\frac{3}{4}\)[/tex] and then multiply it by [tex]\(-\frac{1}{3}\)[/tex].
2. Find the reciprocal: The reciprocal of a fraction is simply flipping its numerator and denominator. Therefore, the reciprocal of [tex]\(-\frac{3}{4}\)[/tex] is [tex]\(-\frac{4}{3}\)[/tex].
3. Rewrite the division as multiplication:
[tex]\[
-\frac{1}{3} \div \left(-\frac{3}{4}\right) \quad \text{becomes} \quad -\frac{1}{3} \times \left(-\frac{4}{3}\right)
\][/tex]
4. Multiply the numerators: For the expression [tex]\(-\frac{1}{3} \times -\frac{4}{3}\)[/tex], we multiply the numerators [tex]\(-1\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-1 \times -4 = 4
\][/tex]
5. Multiply the denominators: Next, we multiply the denominators [tex]\(3\)[/tex] and [tex]\(3\)[/tex]:
[tex]\[
3 \times 3 = 9
\][/tex]
6. Form the resulting fraction: Combining the results from steps 4 and 5, we get:
[tex]\[
\frac{4}{9}
\][/tex]
Thus, the final result of [tex]\(-\frac{1}{3} \div \left(-\frac{3}{4}\right)\)[/tex] is:
[tex]\[
\frac{4}{9}
\][/tex]
In decimal form, [tex]\(\frac{4}{9}\)[/tex] is approximately:
[tex]\[
0.4444444444444444
\][/tex]
So, [tex]\(-\frac{1}{3} \div \left(-\frac{3}{4}\right) = 0.4444444444444444\)[/tex].
