Compare `(5)/(3) and (6)/(5).`

Answer

To compare the rational numbers \( \frac{5}{3} \) and \( \frac{6}{5} \), we can follow these steps:

### Step 1: Convert the fractions to decimal form
To compare the two fractions, we can convert them into decimal form by performing the division.

1. **Calculate \( \frac{6}{5} \)**:
- Divide 6 by 5.
- \( 6 \div 5 = 1.2 \)

2. **Calculate \( \frac{5}{3} \)**:
- Divide 5 by 3.
- \( 5 \div 3 = 1.666... \) (which can be approximated as 1.67)

### Step 2: Compare the decimal values
Now that we have the decimal equivalents:
- \( \frac{6}{5} = 1.2 \)
- \( \frac{5}{3} = 1.666... \)

### Step 3: Determine which is greater
Now we compare the two decimal values:
- \( 1.666... \) (which is \( \frac{5}{3} \)) is greater than \( 1.2 \) (which is \( \frac{6}{5} \)).

### Conclusion
Thus, we can conclude that:
\[ \frac{5}{3} > \frac{6}{5} \]

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