College

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

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

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

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

Answer :

To compare the fractions and order them from least to greatest, we need to look at the fractions given in each option and convert them into decimal numbers to make them easy to compare. Here are the fractions in each option:

Option A:
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]

Option B:
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]

Option C:
- [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(\frac{14}{15}\)[/tex]
- [tex]\(\frac{7}{12}\)[/tex]

Let's analyze the fractions:

1. Fraction [tex]\(\frac{3}{10}\)[/tex]
- Decimal: [tex]\(0.3\)[/tex]

2. Fraction [tex]\(\frac{7}{12}\)[/tex]
- Decimal: [tex]\(0.5833... \approx 0.58\)[/tex]

3. Fraction [tex]\(\frac{5}{6}\)[/tex]
- Decimal: [tex]\(0.8333... \approx 0.83\)[/tex]

4. Fraction [tex]\(\frac{14}{15}\)[/tex]
- Decimal: [tex]\(0.9333... \approx 0.93\)[/tex]

Now, placing these decimals in order from least to greatest:

- [tex]\(0.3\)[/tex] corresponds to [tex]\(\frac{3}{10}\)[/tex]
- [tex]\(0.5833...\)[/tex] corresponds to [tex]\(\frac{7}{12}\)[/tex]
- [tex]\(0.8333...\)[/tex] corresponds to [tex]\(\frac{5}{6}\)[/tex]
- [tex]\(0.9333...\)[/tex] corresponds to [tex]\(\frac{14}{15}\)[/tex]

So, the order of the fractions from least to greatest is:

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

This sequence of fractions is present in Option A:

[tex]\[
\text{Option A:} \quad \frac{3}{10}, \frac{7}{12}, \frac{5}{6}, \frac{14}{15}
\][/tex]

Therefore, Option A is the correct choice for ordering these fractions from least to greatest.

Other Questions