To solve the division problem [tex]$\frac{-15/5}{3/5}$[/tex] step-by-step:
1. Simplify the dividend and the divisor:
- The dividend is [tex]\(\frac{-15}{5}\)[/tex]. Simplifying this fraction results in [tex]\(-3\)[/tex] because [tex]\(\frac{-15}{5} = -3\)[/tex].
- The divisor is [tex]\(\frac{3}{5}\)[/tex].
2. Set up the division problem:
- We need to divide [tex]\(-3\)[/tex] by [tex]\(\frac{3}{5}\)[/tex].
3. Convert the division of fractions to multiplication:
- Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{3}{5}\)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
- So, [tex]\(\frac{-3}{\frac{3}{5}} = -3 \times \frac{5}{3}\)[/tex].
4. Perform the multiplication:
- Multiply [tex]\(-3\)[/tex] by [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[
-3 \times \frac{5}{3} = -3 \times \frac{5}{3} = -\frac{15}{3}
\][/tex]
5. Simplify the resulting fraction:
- Simplify [tex]\(-\frac{15}{3}\)[/tex]:
[tex]\[
-\frac{15}{3} = -5
\][/tex]
Thus, the result of dividing [tex]\(\frac{-15}{5}\)[/tex] by [tex]\(\frac{3}{5}\)[/tex] is [tex]\(-5\)[/tex].
So the correct answer is [tex]\(-5\)[/tex].
