Which one is the largest among the fractions `((5)/(113)),((7)/(120)) ((13)/(145)) and ((17)/(160))?`

Options

A. a) `(5)/(113)`
B. b) `(7)/(720)`
C. c) `(13)/(145)`
D. d) `(17)/(160)`

Answer

To determine which fraction is the largest among \(\frac{5}{113}\), \(\frac{7}{120}\), \(\frac{13}{145}\), and \(\frac{17}{160}\), we can convert each fraction into its decimal form or compare them by cross-multiplying. Here, we'll calculate the decimal values for clarity.

### Step 1: Calculate the decimal value of each fraction

1. **For \(\frac{5}{113}\)**:
\[ \frac{5}{113} \approx 0.044 \]

2. **For \(\frac{7}{120}\)**:
\[ \frac{7}{120} \approx 0.0583 \]

3. **For \(\frac{13}{145}\)**:
\[ \frac{13}{145} \approx 0.0897 \]

4. **For \(\frac{17}{160}\)**:
\[ \frac{17}{160} \approx 0.10625 \]

### Step 2: Compare the decimal values

Now, we can list the decimal values we calculated:
- \(\frac{5}{113} \approx 0.044\)
- \(\frac{7}{120} \approx 0.0583\)
- \(\frac{13}{145} \approx 0.0897\)
- \(\frac{17}{160} \approx 0.10625\)

### Step 3: Identify the largest value

From the decimal values:
- \(0.044\) (for \(\frac{5}{113}\))
- \(0.0583\) (for \(\frac{7}{120}\))
- \(0.0897\) (for \(\frac{13}{145}\))
- \(0.10625\) (for \(\frac{17}{160}\))

The largest value is \(0.10625\), which corresponds to the fraction \(\frac{17}{160}\).

### Conclusion

Thus, the largest fraction among \(\frac{5}{113}\), \(\frac{7}{120}\), \(\frac{13}{145}\), and \(\frac{17}{160}\) is:
\[ \frac{17}{160} \]