Which is greater : `(123)/(250) or (171)/(340)`?

Answer

To determine which fraction is greater between \( \frac{123}{250} \) and \( \frac{171}{340} \), we can use cross-multiplication. This method allows us to compare the two fractions without needing to convert them to decimal form.

### Step-by-Step Solution:

1. **Write down the fractions**:
\[ \frac{123}{250} \quad \text{and} \quad \frac{171}{340} \]

2. **Cross-multiply**:
We will multiply the numerator of the first fraction by the denominator of the second fraction and vice versa.
\[ 123 \times 340 \quad \text{and} \quad 171 \times 250 \]

3. **Calculate the products**:
- For \( 123 \times 340 \):
\[ 123 \times 340 = 41820 \]
- For \( 171 \times 250 \):
\[ 171 \times 250 = 42750 \]

4. **Compare the results**:
Now we compare the two products:
\[ 41820 \quad \text{and} \quad 42750 \]
Since \( 41820 < 42750 \), we conclude that:
\[ \frac{123}{250} < \frac{171}{340} \]

5. **Final conclusion**:
Therefore, \( \frac{171}{340} \) is greater than \( \frac{123}{250} \).

### Answer:
\[ \frac{171}{340} \text{ is greater than } \frac{123}{250}. \]