To solve the division problem
[tex]\[
\frac{15}{4} \div \left( -\frac{5}{8} \right)
\][/tex]
we need to recall that dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of the fraction [tex]\(-\frac{5}{8}\)[/tex] is obtained by swapping the numerator and the denominator, while keeping the sign the same. Therefore, the reciprocal of [tex]\(-\frac{5}{8}\)[/tex] is:
[tex]\[
-\frac{8}{5}
\][/tex]
So, the correct reciprocal fraction to use is:
[tex]\[
-\frac{8}{5}
\][/tex]
Now, instead of dividing by [tex]\(-\frac{5}{8}\)[/tex], we will multiply by its reciprocal:
[tex]\[
\frac{15}{4} \times -\frac{8}{5}
\][/tex]
Next, we perform the multiplication of these fractions:
[tex]\[
\frac{15 \times (-8)}{4 \times 5} = \frac{-120}{20} = -6
\][/tex]
Therefore, the answer to the division problem [tex]\(\frac{15}{4} \div \left( -\frac{5}{8} \right)\)[/tex] is [tex]\(-1.6\)[/tex].
