Question

Identify the numeric order of these fractions and mixed numbers from smallest to largest: 136
, 235
, 79
, 178
.(1 point)
Responses

1315
, 158
, 96
, 79
Start Fraction 13 over 15 End Fraction , Start Fraction 15 over 8 End Fraction , Start Fraction 9 over 6 End Fraction , Start Fraction 7 over 9 End Fraction

235
, 178
, 136
, 79
2 Start Fraction 3 over 5 End Fraction , 1 Start Fraction 7 over 8 End Fraction , 1 Start Fraction 3 over 6 End Fraction , Start Fraction 7 over 9 End Fraction

79
, 106
, 1618
, 135
Start Fraction 7 over 9 End Fraction , Start Fraction 10 over 6 End Fraction , Start Fraction 16 over 18 End Fraction , Start Fraction 13 over 5 End Fraction

79
, 136
, 178
, 235

Answer 1

To compare the given fractions and mixed numbers, let's first convert all the mixed numbers to improper fractions (if applicable) and then evaluate their decimal values:

1. **Responses**:
- Start Fraction 13 over 15 End Fraction = \( \frac{13}{15} \) ≈ 0.8667
- Start Fraction 15 over 8 End Fraction = \( \frac{15}{8} = 1.875 \)
- Start Fraction 9 over 6 End Fraction = \( \frac{9}{6} = 1.5 \)
- Start Fraction 7 over 9 End Fraction = \( \frac{7}{9} \) ≈ 0.7778

2. **Order from smallest to largest**:
- \( \frac{7}{9} \) ≈ 0.7778 (smallest)
- \( \frac{13}{15} \) ≈ 0.8667
- \( \frac{9}{6} = 1.5 \)
- \( \frac{15}{8} = 1.875 \) (largest)

So, the order for the first set of responses is:
- Start Fraction 7 over 9 End Fraction
- Start Fraction 13 over 15 End Fraction
- Start Fraction 9 over 6 End Fraction
- Start Fraction 15 over 8 End Fraction

Now, let's check the other options and evaluate their order as well.

3. **Responses** (Option 2):
- 2 Start Fraction 3 over 5 End Fraction = \( 2 + \frac{3}{5} \) = \( \frac{10}{5} + \frac{3}{5} = \frac{13}{5} \) = 2.6
- 1 Start Fraction 7 over 8 End Fraction = \( 1 + \frac{7}{8} \) = \( \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \) = 1.875
- 1 Start Fraction 3 over 6 End Fraction = \( 1 + \frac{1}{2} = 1.5 \)
- Start Fraction 7 over 9 End Fraction = \( \frac{7}{9} \) ≈ 0.7778

4. **Order for Option 2**:
- \( \frac{7}{9} \) ≈ 0.7778
- \( 1 + \frac{3}{6} = 1.5 \)
- \( 1 + \frac{7}{8} = 1.875 \)
- \( 2 + \frac{3}{5} = 2.6 \)

Next for Option 3 and 4:

5. **Responses** (Option 3):
- 79 = 79
- Start Fraction 10 over 6 End Fraction = \( \frac{10}{6} = 1.6667 \)
- 16 over 18 = \( \frac{16}{18} \) = \( \frac{8}{9} \) ≈ 0.8889
- Start Fraction 13 over 5 End Fraction = \( \frac{13}{5} = 2.6 \)

**Order for Option 3**:
1. 79
2. \( \frac{8}{9} \) ≈ 0.8889
3. \( \frac{10}{6} \) = 1.6667
4. \( \frac{13}{5} \) = 2.6

6. **Responses** (Option 4):
- 79
- 136
- 178
- 235

**Final Numeric Order**:
After evaluating all options, the order from smallest to largest (using the values given) is:

1. Response with fractions:
- 79
- Start Fraction 7 over 9 End Fraction
- Start Fraction 13 over 15 End Fraction
- Start Fraction 9 over 6 End Fraction
- Start Fraction 15 over 8 End Fraction
2. 79, 136, 178, 235 directly listed is also correct.

The smallest to largest of the given choices:
- **79, 136, 178, 235**