Let's break down the solution step by step.
### First Term Estimate
First, calculate the fraction [tex]\(\frac{200 + 0 + 8}{500 + 60 + 4}\)[/tex].
1. Numerator Calculation:
[tex]\[
200 + 0 + 8 = 208
\][/tex]
2. Denominator Calculation:
[tex]\[
500 + 60 + 4 = 564
\][/tex]
3. Fraction Evaluation:
[tex]\[
\frac{208}{564} \approx 0.3688
\][/tex]
### Second Term Estimate
Next, compute the fraction [tex]\(\frac{277}{700 + 60 + 17}\)[/tex].
1. Numerator Calculation:
[tex]\[
\text{Numerator} = 277
\][/tex]
2. Denominator Calculation:
[tex]\[
700 + 60 + 17 = 777
\][/tex]
3. Fraction Evaluation:
[tex]\[
\frac{277}{777} \approx 0.3565
\][/tex]
### Summation of Both Terms
Finally, sum the two evaluated fractions:
[tex]\[
0.3688 + 0.3565 \approx 0.7253
\][/tex]
### Conclusion
So, the estimated value of the given expression [tex]\(\frac{200 + 0 + 8}{500 + 60 + 4} + \frac{277}{700 + 60 + 17}\)[/tex] is approximately [tex]\(0.7253\)[/tex]:
[tex]\[
\boxed{0.7253}
\][/tex]
