Sure, let's evaluate the expression step-by-step. The expression we need to evaluate is:
[tex]\[
\frac{3}{7} + \left( \frac{-6}{11} \right) + \left( \frac{-8}{21} \right) + \frac{5}{22}
\][/tex]
1. Convert each fraction to a decimal:
[tex]\[
\frac{3}{7} \approx 0.42857142857142855
\][/tex]
[tex]\[
\frac{-6}{11} \approx -0.5454545454545454
\][/tex]
[tex]\[
\frac{-8}{21} \approx -0.38095238095238093
\][/tex]
[tex]\[
\frac{5}{22} \approx 0.22727272727272727
\][/tex]
2. Sum these decimal values:
[tex]\[
0.42857142857142855 + (-0.5454545454545454) + (-0.38095238095238093) + 0.22727272727272727
\][/tex]
3. Add them sequentially:
- First two fractions:
[tex]\[
0.42857142857142855 + (-0.5454545454545454) \approx -0.11688311688311685
\][/tex]
- Adding the third fraction:
[tex]\[
-0.11688311688311685 + (-0.38095238095238093) \approx -0.4978354978354978
\][/tex]
- Finally, adding the fourth fraction:
[tex]\[
-0.4978354978354978 + 0.22727272727272727 \approx -0.27056277056277056
\][/tex]
So, the sum of the given fractions is:
[tex]\[
\frac{3}{7} + \left( \frac{-6}{11} \right) + \left( \frac{-8}{21} \right) + \frac{5}{22} \approx -0.27056277056277056
\][/tex]
