Which of the following is correct?

Question

Accepted Answer

To determine why Option 4 is correct, we need to compare the fractions 4/7, 3/5, and 8/9. Let's convert these fractions to decimal form for easier comparison:

1. **4/7**: To convert 4/7 to a decimal, divide 4 by 7, which equals approximately 0.5714.
2. **3/5**: To convert 3/5 to a decimal, divide 3 by 5, which equals 0.6.
3. **8/9**: To convert 8/9 to a decimal, divide 8 by 9, which equals approximately 0.8889.

Now, let's compare these decimal values:

- 4/7 (0.5714) is less than 3/5 (0.6).
- 3/5 (0.6) is less than 8/9 (0.8889).

Therefore, the correct order from smallest to largest is 4/7 < 3/5 < 8/9, which corresponds to Option 4.

### Explanation of Incorrect Options:

1. **Option 1: 3/5 < 4/7 < 8/9**
   - This option is incorrect because 3/5 (0.6) is actually greater than 4/7 (0.5714), not less.

2. **Option 2: 4/7 < 8/9 < 3/5**
   - This option is incorrect because 8/9 (0.8889) is greater than 3/5 (0.6), not less.

3. **Option 3: 3/5 < 8/9 < 4/7**
   - This option is incorrect because 4/7 (0.5714) is less than 3/5 (0.6), not greater.

By following the logical comparison of the decimal values, we can confidently conclude that Option 4 is the correct answer, as it accurately represents the order of the fractions from smallest to largest.