A rational number between 5/7 and 9/11 is .

• A 59/77
• B 31/77
• C 23/11
• D 7/9

To find a rational number between the fractions 5/7 and 9/11, we first need to convert them to a common denominator or compare their decimal values.

Step 1: Convert to Decimal

Calculating the decimal values:

• 5/7 ≈ 0.7143
• 9/11 ≈ 0.8181

Step 2: Identify the Range

Now, we need a number that falls between 0.7143 and 0.8181.

Step 3: Evaluate the Options

Let's check the given options:

• A) 59/77 ≈ 0.7662
• B) 31/77 ≈ 0.4026
• C) 23/11 ≈ 2.0909
• D) 7/9 ≈ 0.7778

Step 4: Determine Valid Choices

The fractions 59/77 and 7/9 both fall between 5/7 and 9/11:

• 59/77 is approximately 0.7662, which is between 0.7143 and 0.8181.
• 7/9 is approximately 0.7778, also between 0.7143 and 0.8181.

Final Answer

Therefore, both 59/77 and 7/9 are valid rational numbers between 5/7 and 9/11. If you need just one option, you can choose 59/77.