Question

Identify the numeric order of these fractions and Mixed numbers from smallest to largest:1 3/6, 2 3/5, 7/9, 1 7/8. (1 point) Responses.
13/15, 15/8, 9/6, 7/9
2 3/5, 1 7/8, 1 3/6, 7/9
7/9, 1 3/6, 1 7/8, 2 3/5
7/9, 10/6, 16/18, 13/5

Answer 1

To order the given fractions and mixed numbers (1 3/6, 2 3/5, 7/9, 1 7/8) from smallest to largest, we'll first convert everything to improper fractions or decimals for easier comparison.

1. **Convert Mixed Numbers to Improper Fractions**:
- \(1 \frac{3}{6} = \frac{6+3}{6} = \frac{9}{6} = \frac{3}{2}\)
- \(2 \frac{3}{5} = \frac{10+3}{5} = \frac{13}{5}\)
- \(1 \frac{7}{8} = \frac{8+7}{8} = \frac{15}{8}\)

2. **List the fractions**:
- \(7/9\) (as it is)
- \(\frac{3}{2} = \frac{9}{6}\)
- \(\frac{13}{5}\) (as it is)
- \(\frac{15}{8}\) (as it is)

3. **Convert to a common denominator to compare** or find decimal equivalents:
- \(7/9 \approx 0.777\)
- \(\frac{3}{2} = 1.5\)
- \(\frac{13}{5} = 2.6\)
- \(\frac{15}{8} = 1.875\)

Now in decimal form:
- \(7/9 \approx 0.777\)
- \(1 \frac{7}{8} \approx 1.875\)
- \(1 \frac{3}{6} \approx 1.5\)
- \(2 \frac{3}{5} \approx 2.6\)

4. **Ordering the numbers** by value:
- \(7/9\) (≈ 0.777)
- \(1 \frac{3}{6}\) (1.5)
- \(1 \frac{7}{8}\) (1.875)
- \(2 \frac{3}{5}\) (2.6)

Now, rewriting in ordered form:
- \(7/9\)
- \(1 \frac{3}{6}\)
- \(1 \frac{7}{8}\)
- \(2 \frac{3}{5}\)

The correct order from smallest to largest is:
**7/9, 1 3/6, 1 7/8, 2 3/5**

Thus, the correct response from the options would be:
**7/9, 1 3/6, 1 7/8, 2 3/5**