2 1/3:(5/8-8/3)+2•1 3/7=1,857

Let's solve the expression step by step:

1. Convert mixed numbers to improper fractions:

   • \(2 \frac{1}{3} = \frac{7}{3}\)
   • \(2 \frac{1}{7} = \frac{15}{7}\)

2. Calculate the expression inside the parentheses:

   • \(\frac{5}{8} - \frac{8}{3}\)
   • To subtract these fractions, find a common denominator. The least common multiple of 8 and 3 is 24.

   Convert both fractions:

   • \(\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}\)
   • \(\frac{8}{3} = \frac{8 \times 8}{3 \times 8} = \frac{64}{24}\)

   Now perform the subtraction: \[ \frac{5}{8} - \frac{8}{3} = \frac{15}{24} - \frac{64}{24} = \frac{15 - 64}{24} = \frac{-49}{24} \]

3. Perform the division:

   • We have \(\frac{7}{3} : \left(\frac{-49}{24}\right)\)
   • Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{7}{3} \div \frac{-49}{24} = \frac{7}{3} \times \frac{24}{-49} \]
   • Calculate: \[ = \frac{7 \times 24}{3 \times -49} = \frac{168}{-147} = -\frac{24}{21} = -\frac{8}{7} \]

4. Calculate the multiplication:

   • Calculate \(2 \cdot \frac{15}{7}\): \[ 2 \cdot \frac{15}{7} = \frac{30}{7} \]

5. Add the results:

   • We need to combine \(-\frac{8}{7}\) and \(\frac{30}{7}\): \[ -\frac{8}{7} + \frac{30}{7} = \frac{30 - 8}{7} = \frac{22}{7} \]

6. Convert to decimal:

   • Now convert \(\frac{22}{7}\) to decimal form: \[ \frac{22}{7} \approx 3.14 \]

Thus, the calculated value of the expression \( 2 \frac{1}{3} : ( \frac{5}{8} - \frac{8}{3}) + 2 \cdot 2 \frac{1}{7} \) is approximately \( 3.14 \), not \( 1.857 \).

If you intended to arrive at \( 1.857 \), please verify or provide more context or corrections regarding input numbers or operations.