Answer :
To solve the problem of ordering the fractions from least to greatest, let's analyze each option and determine which one shows the correct order.
### Fractions to Consider:
1. Option A:
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
2. Option B:
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
3. Option C:
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
### Steps to Order Fractions:
1. Convert Each Fraction to a Decimal:
- [tex]\(\frac{3}{10} = 0.3\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
- [tex]\(\frac{7}{12} \approx 0.5833\)[/tex]
- [tex]\(\frac{14}{15} \approx 0.9333\)[/tex]
2. Rank the Decimals:
- 0.3 is the smallest
- 0.5833
- 0.8333
- 0.9333 is the largest
The correct order of the fractions from least to greatest based on their decimal values is:
[tex]\[\frac{3}{10}, \frac{7}{12}, \frac{5}{6}, \frac{14}{15}\][/tex]
### Evaluate Each Option:
- Option A: [tex]\(\frac{3}{10}, \frac{5}{6}, \frac{7}{12}, \frac{14}{15}\)[/tex]
- This is not sorted correctly as [tex]\(\frac{5}{6}\)[/tex] appears before [tex]\(\frac{7}{12}\)[/tex].
- Option B: [tex]\(\frac{3}{10}, \frac{7}{12}, \frac{5}{6}, \frac{14}{15}\)[/tex]
- This is sorted correctly from least to greatest.
- Option C: [tex]\(\frac{5}{6}, \frac{3}{10}, \frac{14}{15}, \frac{7}{12}\)[/tex]
- This is not sorted correctly.
Therefore, Option B lists the fractions in order from least to greatest correctly.
### Fractions to Consider:
1. Option A:
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
2. Option B:
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
3. Option C:
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
### Steps to Order Fractions:
1. Convert Each Fraction to a Decimal:
- [tex]\(\frac{3}{10} = 0.3\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
- [tex]\(\frac{7}{12} \approx 0.5833\)[/tex]
- [tex]\(\frac{14}{15} \approx 0.9333\)[/tex]
2. Rank the Decimals:
- 0.3 is the smallest
- 0.5833
- 0.8333
- 0.9333 is the largest
The correct order of the fractions from least to greatest based on their decimal values is:
[tex]\[\frac{3}{10}, \frac{7}{12}, \frac{5}{6}, \frac{14}{15}\][/tex]
### Evaluate Each Option:
- Option A: [tex]\(\frac{3}{10}, \frac{5}{6}, \frac{7}{12}, \frac{14}{15}\)[/tex]
- This is not sorted correctly as [tex]\(\frac{5}{6}\)[/tex] appears before [tex]\(\frac{7}{12}\)[/tex].
- Option B: [tex]\(\frac{3}{10}, \frac{7}{12}, \frac{5}{6}, \frac{14}{15}\)[/tex]
- This is sorted correctly from least to greatest.
- Option C: [tex]\(\frac{5}{6}, \frac{3}{10}, \frac{14}{15}, \frac{7}{12}\)[/tex]
- This is not sorted correctly.
Therefore, Option B lists the fractions in order from least to greatest correctly.