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Select the proper order from least to greatest for [tex]\( \frac{2}{3}, \frac{7}{6}, \frac{1}{8}, \frac{9}{10} \)[/tex].

A. [tex]\( \frac{2}{3}, \frac{9}{10}, \frac{7}{6}, \frac{1}{8} \)[/tex]

B. [tex]\( \frac{7}{6}, \frac{9}{10}, \frac{2}{3}, \frac{1}{8} \)[/tex]

C. [tex]\( \frac{1}{8}, \frac{9}{10}, \frac{7}{6}, \frac{2}{3} \)[/tex]

D. [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex]

Sagot :

GinnyAnswer
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 compare their decimal equivalents.

- [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
- [tex]\( \frac{7}{6} \approx 1.1667 \)[/tex]
- [tex]\( \frac{1}{8} = 0.125 \)[/tex]
- [tex]\( \frac{9}{10} = 0.9 \)[/tex]

By comparing these decimal values, we can arrange the fractions in ascending order:

1. [tex]\( \frac{1}{8} \approx 0.125 \)[/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]

Therefore, the proper order from least to greatest is [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex].

The correct answer is:

D. [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex].
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