To determine which of the given options contains unlike fractions, we need to analyze each option based on the definition of unlike fractions. Unlike fractions are fractions that do not have the same denominator.
### Step-by-Step Solution:
1. **Identify the first option:**
The first option is \( \frac{1}{17}, \frac{3}{51}, \frac{3}{17} \).
- Check the denominators:
- The denominators are 17, 51, and 17.
- Since \( \frac{3}{51} \) can be simplified to \( \frac{1}{17} \) (because \( 3 \div 3 = 1 \) and \( 51 \div 3 = 17 \)), all fractions can be expressed with the same denominator (17).
- Therefore, this option does not contain unlike fractions.
2. **Identify the second option:**
The second option is \( \frac{4}{9}, \frac{2}{18}, \frac{5}{9} \).
- Check the denominators:
- The denominators are 9, 18, and 9.
- Simplify \( \frac{2}{18} \):
- \( \frac{2}{18} = \frac{1}{9} \) (because \( 2 \div 2 = 1 \) and \( 18 \div 2 = 9 \)).
- Now the fractions are \( \frac{4}{9}, \frac{1}{9}, \frac{5}{9} \), all with the same denominator (9).
- Therefore, this option does not contain unlike fractions.
3. **Identify the third option:**
The third option is \( \frac{4}{15}, \frac{16}{19}, \frac{17}{36} \).
- Check the denominators:
- The denominators are 15, 19, and 36.
- None of these fractions can be simplified further, and they all have different denominators.
- Therefore, this option contains unlike fractions.
### Conclusion:
The third option \( \frac{4}{15}, \frac{16}{19}, \frac{17}{36} \) contains unlike fractions.
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