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13. 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{1}{8}, \frac{9}{10}, \frac{7}{6}, \frac{2}{3}[/tex]

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

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

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



Answer :

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 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]

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