Which is greater \( 23 / 4 \) or \( 57 / 8 \) ?

To determine which fraction is greater between \( \frac{23}{4} \) and \( \frac{57}{8} \), we can compare them in a couple of ways: by converting them to decimals or by finding a common denominator. ### Method 1: Converting to Decimals 1. **Convert \( \frac{23}{4} \) to a decimal:** \[ \frac{23}{4} = 5.75 \] 2. **Convert \( \frac{57}{8} \) to a decimal:** \[ \frac{57}{8} = 7.125 \] Since \( 7.125 > 5.75 \), \( \frac{57}{8} \) is greater than \( \frac{23}{4} \). ### Method 2: Cross-Multiplication Alternatively, we can compare the two fractions by cross-multiplying to avoid converting to decimals. 1. **Multiply the numerator of the first fraction by the denominator of the second fraction:** \[ 23 \times 8 = 184 \] 2. **Multiply the numerator of the second fraction by the denominator of the first fraction:** \[ 57 \times 4 = 228 \] 3. **Compare the two products:** \[ 228 > 184 \] Since \( 228 > 184 \), it follows that: \[ \frac{57}{8} > \frac{23}{4} \] ### Conclusion Both methods clearly show that: \[ \boxed{\dfrac{57}{8} \text{ is greater than } \dfrac{23}{4}} \]