To determine the proper order from least to greatest for the fractions [tex]\( \frac{2}{3}, \frac{7}{6}, \frac{1}{8}, \frac{9}{10} \)[/tex], let's carefully examine their decimal equivalents, which reflect their values more clearly.
1. [tex]\( \frac{1}{8} = 0.125 \)[/tex]
2. [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
3. [tex]\( \frac{9}{10} = 0.9 \)[/tex]
4. [tex]\( \frac{7}{6} \approx 1.1667 \)[/tex]
Now, let's organize these decimal equivalents from the smallest to the largest:
- 0.125 (corresponds to [tex]\( \frac{1}{8} \)[/tex])
- 0.6667 (corresponds to [tex]\( \frac{2}{3} \)[/tex])
- 0.9 (corresponds to [tex]\( \frac{9}{10} \)[/tex])
- 1.1667 (corresponds to [tex]\( \frac{7}{6} \)[/tex])
Given these values, the proper order of the fractions from least to greatest is:
[tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex]
Thus, the correct answer is:
D. [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex]
