Question

Use the given tables to compare the ratios 3:5 and 2:3 . 3 5 6 10 9 15 12 20 15 25 2 3 4 6 6 9 8 12 10 15 Responses 3:5 > 2:3 3:5 > 2:3 - no response given 3:5 < 2:3 3:5 < 2:3 - no response given 3:5 = 2:3 3:5 = 2:3 - no response given More rows need to be added to the tables to be able to compare the ratios.

Answer 1

To compare the ratios 3:5 and 2:3, we can analyze their values and relationships.

1. Convert Ratios to Decimal Form:

   • For the ratio 3:5: \[ \text{Decimal value} = \frac{3}{5} = 0.6 \]

   • For the ratio 2:3: \[ \text{Decimal value} = \frac{2}{3} \approx 0.6667 \]

2. Comparison:

   • Now that we have both ratios in decimal form:
     • \( 3:5 = 0.6 \)
     • \( 2:3 \approx 0.6667 \)

   Since \( 0.6 < 0.6667 \), we conclude that:

   \[ 3:5 < 2:3 \]

3. Responses Evaluated:

   From your provided responses, we evaluate them as follows:

   • 3:5 > 2:3 (False)
   • 3:5 < 2:3 (True)
   • 3:5 = 2:3 (False)

   Thus, the correct statement is 3:5 < 2:3.

4. Conclusion:

   Based on our calculations and comparisons, the most accurate response would be:

   • 3:5 < 2:3

To compare further, you may add more rows to the tables, representing additional values from each ratio to gather more insights if needed. For example, you could state more fractions and corresponding ratios to test if they keep the same relationship or not.