Sure, let's solve this problem step-by-step.
1. Convert the fractions to decimals:
- For [tex]\( \frac{15}{8} \)[/tex]: [tex]\( \frac{15}{8} = 1.875 \)[/tex]
- For [tex]\( \frac{6}{7} \)[/tex]: [tex]\( \frac{6}{7} \approx 0.8571 \)[/tex] (rounded to four decimal places)
- For [tex]\( \frac{19}{6} \)[/tex]: [tex]\( \frac{19}{6} \approx 3.1667 \)[/tex] (rounded to four decimal places)
- For [tex]\( \frac{8}{3} \)[/tex]: [tex]\( \frac{8}{3} \approx 2.6667 \)[/tex] (rounded to four decimal places)
2. Compute the sum of the first two fractions:
- Sum [tex]\( \frac{15}{8} + \frac{6}{7} \)[/tex]:
[tex]\[ 1.875 + 0.8571 = 2.7321 \][/tex] (rounded to four decimal places)
3. Compute the sum of the next two fractions:
- Sum [tex]\( \frac{19}{6} + \frac{8}{3} \)[/tex]:
[tex]\[ 3.1667 + 2.6667 = 5.8333 \][/tex] (rounded to four decimal places)
4. Divide the sum of the first two fractions by the sum of the next two fractions:
- Compute [tex]\( \frac{2.7321}{5.8333} \)[/tex]:
[tex]\[ \frac{2.7321}{5.8333} \approx 0.4684 \][/tex] (rounded to four decimal places)
Thus, the final result is:
- The sum of [tex]\( \frac{15}{8} \)[/tex] and [tex]\( \frac{6}{7} \)[/tex] is approximately [tex]\( 2.7321 \)[/tex].
- The sum of [tex]\( \frac{19}{6} \)[/tex] and [tex]\( \frac{8}{3} \)[/tex] is approximately [tex]\( 5.8333 \)[/tex].
- Dividing the first sum by the second sum gives approximately [tex]\( 0.4684 \)[/tex].
In summary:
[tex]\[ \frac{2.7321}{5.8333} \approx 0.4684 \][/tex]
