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Estimate:

[tex]\[
\begin{aligned}
208 & \approx \frac{200 + 0 + 8}{500 + 60 + 4} \\
+569 & \approx \frac{277}{700 + 60 + 17}
\end{aligned}
\][/tex]

Sagot :

GinnyAnsweridn
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]
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