To find the value of the given expression:
[tex]\[
\left(2+\frac{2}{3} \div \frac{1}{5} \cdot \frac{4}{7}\right) \div \left(\frac{47}{63} \div \frac{2}{5}\right)
\][/tex]
we will break it down into manageable parts, solving each part step by step.
Step 1: Evaluate [tex]\(\left(2+\frac{2}{3} \div \frac{1}{5} \cdot \frac{4}{7}\right)\)[/tex]
1. Begin by adding [tex]\(\frac{2}{3}\)[/tex] to 2:
[tex]\[
2 + \frac{2}{3} = 2.6666666666666665
\][/tex]
2. Next, consider the part inside the division and multiplication: [tex]\(\frac{1}{5} \cdot \frac{4}{7}\)[/tex]:
[tex]\[
\frac{1}{5} \cdot \frac{4}{7} = 0.11428571428571428
\][/tex]
3. Now, divide the sum [tex]\(2 + \frac{2}{3}\)[/tex] by the product [tex]\(\frac{1}{5} \cdot \frac{4}{7}\)[/tex]:
[tex]\[
\frac{2.6666666666666665}{0.11428571428571428} = 23.333333333333332
\][/tex]
Step 2: Evaluate [tex]\(\left(\frac{47}{63} \div \frac{2}{5}\right)\)[/tex]
1. First, simplify the division by multiplying by the reciprocal:
[tex]\[
\frac{47}{63} \div \frac{2}{5} = \frac{47}{63} \cdot \frac{5}{2} = 1.8650793650793651
\][/tex]
Step 3: Divide the result of Step 1 by the result of Step 2
Now we have:
[tex]\[
\frac{23.333333333333332}{1.8650793650793651} = 12.51063829787234
\][/tex]
Therefore, the value of the given expression [tex]\(\left(2+\frac{2}{3} \div \frac{1}{5} \cdot \frac{4}{7}\right) \div \left(\frac{47}{63} \div \frac{2}{5}\right)\)[/tex] is:
[tex]\[
12.51063829787234
\][/tex]
