To solve the problem of ordering the fractions [tex]\( \frac{2}{3}, \frac{7}{6}, \frac{1}{8}, \frac{9}{10} \)[/tex] from least to greatest, let's break down the solution into clear steps:
### Step-by-Step Solution:
1. Identify the Fractions:
- We have four fractions: [tex]\( \frac{2}{3}, \frac{7}{6}, \frac{1}{8}, \frac{9}{10} \)[/tex].
2. Convert Fractions to Decimal Form:
- [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]
3. Compare the Decimal Values:
- The decimal form of the fractions, from least to greatest, are:
- [tex]\( 0.125 \)[/tex]
- [tex]\( 0.6667 \)[/tex]
- [tex]\( 0.9 \)[/tex]
- [tex]\( 1.1667 \)[/tex]
4. Put the Original Fractions in Order According to Their Decimal Values:
- [tex]\( \frac{1}{8} \)[/tex]
- [tex]\( \frac{2}{3} \)[/tex]
- [tex]\( \frac{9}{10} \)[/tex]
- [tex]\( \frac{7}{6} \)[/tex]
5. Check the Options Given in the Question:
- A. [tex]\( \frac{2}{3}, \frac{9}{10}, \frac{7}{6}, \frac{1}{8} \)[/tex]
- B. [tex]\( \frac{1}{8}, \frac{9}{10}, \frac{7}{6}, \frac{2}{3} \)[/tex]
- C. [tex]\( \frac{7}{6}, \frac{9}{10}, \frac{2}{3}, \frac{1}{8} \)[/tex]
- D. [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex]
6. Select the Correct Order:
- The correct order from least to greatest is [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex].
### Conclusion:
- The best answer for the problem, selecting the proper order from least to greatest, is:
- D. [tex]\( \frac{1}{8}, \frac{2}{3}, \frac{9}{10}, \frac{7}{6} \)[/tex].
