Identify the numeric order of these fractions and mixed numbers from smallest to largest: 136

Question

, 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

5. 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