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



Answer :

GinnyAnswer
To determine the proper order from least to greatest for the fractions \( \frac{2}{3}, \frac{7}{6}, \frac{1}{8}, \frac{9}{10} \), let's go through a step-by-step comparison of their values.

1. Compare \( \frac{2}{3} \) and other fractions:
- \( \frac{2}{3} \approx 0.6667 \)

2. Compare \( \frac{7}{6} \) and other fractions:
- \( \frac{7}{6} \approx 1.1667 \)
- Clearly \( \frac{7}{6} > \frac{2}{3} \)

3. Compare \( \frac{1}{8} \) and other fractions:
- \( \frac{1}{8} = 0.125 \)
- Clearly \( \frac{1}{8} < \frac{2}{3} \) and \( \frac{1}{8} < \frac{7}{6} \)

4. Compare \( \frac{9}{10} \) and other fractions:
- \( \frac{9}{10} = 0.9 \)
- Clearly \( \frac{9}{10} > \frac{2}{3} \) but \( \frac{9}{10} < \frac{7}{6} \)

Thus, arranging these values from least to greatest, we have:
- \( \frac{1}{8} \)
- \( \frac{2}{3} \)
- \( \frac{9}{10} \)
- \( \frac{7}{6} \)

Hence, the proper order from least to greatest is:

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

So, the correct answer is [tex]\( \boxed{B} \)[/tex].

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