Use the given tables to compare the ratios 3:5 and 2:3

Question

The 3 to 5 table goes up to 15 and 25
The 2 to 3 table goes up to 10 and 15
• 3:5>2:3
•3:5=2:3
•3:5<2:3

Answer 1

To compare the ratios 3:5 and 2:3, let's create the multiplication tables for both ratios based on the provided limits.

For the ratio 3:5:

• Multiplying by 1: 3 * 1 = 3, 5 * 1 = 5 → (3, 5)
• Multiplying by 2: 3 * 2 = 6, 5 * 2 = 10 → (6, 10)
• Multiplying by 3: 3 * 3 = 9, 5 * 3 = 15 → (9, 15)
• Multiplying by 4: 3 * 4 = 12, 5 * 4 = 20 → (12, 20)
• Multiplying by 5: 3 * 5 = 15, 5 * 5 = 25 → (15, 25)

For the ratio 2:3:

• Multiplying by 1: 2 * 1 = 2, 3 * 1 = 3 → (2, 3)
• Multiplying by 2: 2 * 2 = 4, 3 * 2 = 6 → (4, 6)
• Multiplying by 3: 2 * 3 = 6, 3 * 3 = 9 → (6, 9)
• Multiplying by 4: 2 * 4 = 8, 3 * 4 = 12 → (8, 12)
• Multiplying by 5: 2 * 5 = 10, 3 * 5 = 15 → (10, 15)

Comparison:

To compare the ratios, we can look at their values or cross-multiply.

For example, we can compare the values:

• Take the first values of both ratios:
  • 3:5 → 3/5 = 0.6
  • 2:3 → 2/3 ≈ 0.6667

Since 0.6 < 0.6667, we can conclude:

3:5 < 2:3

Thus, the correct statement is:

• 3:5 < 2:3.