To solve the problem [tex]\(8 \div 2 \frac{2}{9} - 2 \frac{11}{15}\)[/tex], let us follow a step-by-step process.
1. Convert the mixed numbers to improper fractions:
- [tex]\(2 \frac{2}{9}\)[/tex]:
[tex]\[
2 \frac{2}{9} = 2 + \frac{2}{9} = \frac{18}{9} + \frac{2}{9} = \frac{20}{9}
\][/tex]
2. Divide 8 by [tex]\(2 \frac{2}{9}\)[/tex]:
- [tex]\(2 \frac{2}{9} = 2.2222222222222223\)[/tex]
- Dividing 8 by [tex]\(2 \frac{2}{9}\)[/tex]:
[tex]\[
8 \div 2 \frac{2}{9} = 8 \div 2.2222222222222223 \approx 3.5999999999999996
\][/tex]
3. Convert the second mixed number ([tex]\(2 \frac{11}{15}\)[/tex]) to an improper fraction:
- [tex]\(2 \frac{11}{15}\)[/tex]:
[tex]\[
2 \frac{11}{15} = 2 + \frac{11}{15} = \frac{30}{15} + \frac{11}{15} = \frac{41}{15}
\][/tex]
- [tex]\(2 \frac{11}{15} = 2.7333333333333334\)[/tex]
4. Subtract the second value from the result of the division:
- Result of the division: [tex]\(3.5999999999999996\)[/tex]
- Value to subtract: [tex]\(2.7333333333333334\)[/tex]
- Perform the subtraction:
[tex]\[
3.5999999999999996 - 2.7333333333333334 \approx 0.8666666666666663
\][/tex]
So, the answer to [tex]\(8 \div 2 \frac{2}{9} - 2 \frac{11}{15}\)[/tex] is:
[tex]\[
\boxed{0.8666666666666663}
\][/tex]
