Let's resolve the given operations step-by-step.
### Part (a)
We are given the operation:
[tex]\[
\left(\frac{12}{5}\right) \div\left(-\frac{3}{10}\right)
\][/tex]
To divide fractions, we multiply by the reciprocal of the divisor. Thus, we have:
[tex]\[
\left(\frac{12}{5}\right) \div \left(-\frac{3}{10}\right) = \left(\frac{12}{5}\right) \times \left(-\frac{10}{3}\right)
\][/tex]
Now we perform the multiplication of fractions by multiplying the numerators together and the denominators together:
[tex]\[
\frac{12 \times -10}{5 \times 3} = \frac{-120}{15}
\][/tex]
Next, we simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 15:
[tex]\[
\frac{-120 \div 15}{15 \div 15} = \frac{-8}{1} = -8
\][/tex]
Thus, the result of part (a) is:
[tex]\[
-8
\][/tex]
### Part (b)
We are given the operation:
[tex]\[
\left(-\frac{15}{8}\right) \div \left(-\frac{5}{4}\right)
\][/tex]
To divide fractions, we multiply by the reciprocal of the divisor. Thus, we have:
[tex]\[
\left(-\frac{15}{8}\right) \div \left(-\frac{5}{4}\right) = \left(-\frac{15}{8}\right) \times \left(-\frac{4}{5}\right)
\][/tex]
Now we perform the multiplication of fractions by multiplying the numerators together and the denominators together:
[tex]\[
\frac{(-15) \times (-4)}{8 \times 5} = \frac{60}{40}
\][/tex]
Next, we simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 20:
[tex]\[
\frac{60 \div 20}{40 \div 20} = \frac{3}{2}
\][/tex]
Thus, the result of part (b) is:
[tex]\[
\frac{3}{2} \quad \text{or} \quad 1.5
\][/tex]
### Final Results
- Part (a): [tex]\(-8\)[/tex]
- Part (b): [tex]\(\frac{3}{2}\)[/tex] or [tex]\(1.5\)[/tex]
These detailed steps provide the solutions to the given operations.
