Sure! Let's solve the problem step-by-step.
1. Understand the problem: We need to multiply the fraction [tex]\(\frac{7}{13}\)[/tex] by the reciprocal of [tex]\(-7116\)[/tex].
2. Find the reciprocal of -7116: The reciprocal of a number [tex]\(a\)[/tex] is given by [tex]\(\frac{1}{a}\)[/tex]. Therefore, the reciprocal of [tex]\(-7116\)[/tex] is [tex]\(\frac{1}{-7116}\)[/tex].
3. Express the reciprocal: [tex]\(\frac{1}{-7116}\)[/tex] can be written as [tex]\(-\frac{1}{7116}\)[/tex], which is approximately [tex]\(-0.0001405283867341203\)[/tex].
4. Multiply [tex]\(\frac{7}{13}\)[/tex] by [tex]\(\frac{1}{-7116}\)[/tex]:
[tex]\[
\frac{7}{13} \times -0.0001405283867341203 = -7.566913131837246 \times 10^{-5}
\][/tex]
Therefore, the solution involves:
- Finding the reciprocal of -7116, which is approximately [tex]\(-0.0001405283867341203\)[/tex],
- Multiplying [tex]\(\frac{7}{13}\)[/tex] by this reciprocal, resulting in approximately [tex]\(-7.566913131837246 \times 10^{-5}\)[/tex].
So, the final result of multiplying [tex]\(\frac{7}{13}\)[/tex] by the reciprocal of [tex]\(-7116\)[/tex] is approximately [tex]\(-7.566913131837246 \times 10^{-5}\)[/tex].
