Which of the following fractions are equivalent:
`14/(77), 2/(11)`

Answer

To determine whether the fractions \( \frac{14}{77} \) and \( \frac{2}{11} \) are equivalent, we can follow these steps:

### Step 1: Simplify \( \frac{14}{77} \)

To simplify \( \frac{14}{77} \), we need to find the greatest common divisor (GCD) of the numerator (14) and the denominator (77).

- The factors of 14 are: 1, 2, 7, 14
- The factors of 77 are: 1, 7, 11, 77

The greatest common factor is 7.

Now, we divide both the numerator and the denominator by their GCD (7):

\[ \frac{14 \div 7}{77 \div 7} = \frac{2}{11} \]

### Step 2: Compare the simplified fraction with \( \frac{2}{11} \)

Now that we have simplified \( \frac{14}{77} \) to \( \frac{2}{11} \), we can see that:

\[ \frac{14}{77} = \frac{2}{11} \]

### Conclusion

Since both fractions are equal after simplification, we conclude that:

\[ \frac{14}{77} \text{ is equivalent to } \frac{2}{11} \]

### Final Answer
The fractions \( \frac{14}{77} \) and \( \frac{2}{11} \) are equivalent.

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