College

Choose the sequence that orders the fractions from least to greatest.

A.
[tex]\[
\begin{array}{cccc}
\frac{3}{10} & \frac{5}{6} & \frac{7}{12} & \frac{14}{15} \\
\end{array}
\][/tex]

B.
[tex]\[
\frac{3}{10}, \frac{7}{12}, \frac{5}{6}, \frac{14}{15}
\][/tex]

C.
[tex]\[
\begin{array}{c|c|c|c}
\frac{5}{6} & \frac{3}{10} & \frac{14}{15} & \frac{7}{12} \\
\end{array}
\][/tex]

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.

Other Questions