Which of the following fractions are equivalent:
`2/(6), 14/(42)`

Answer

To determine if the fractions \( \frac{2}{6} \) and \( \frac{14}{42} \) are equivalent, we can simplify each fraction and see if they are equal.

### Step 1: Simplify \( \frac{2}{6} \)
To simplify \( \frac{2}{6} \), we need to find the greatest common divisor (GCD) of the numerator (2) and the denominator (6).

- The factors of 2 are: 1, 2
- The factors of 6 are: 1, 2, 3, 6

The GCD of 2 and 6 is 2. Now, we divide both the numerator and the denominator by their GCD.

\[ \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \]

### Step 2: Simplify \( \frac{14}{42} \)
Next, we simplify \( \frac{14}{42} \) by finding the GCD of 14 and 42.

- The factors of 14 are: 1, 2, 7, 14
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The GCD of 14 and 42 is 14. Now, we divide both the numerator and the denominator by their GCD.

\[ \frac{14 \div 14}{42 \div 14} = \frac{1}{3} \]

### Conclusion
Both fractions simplify to \( \frac{1}{3} \). Therefore, the fractions \( \frac{2}{6} \) and \( \frac{14}{42} \) are equivalent.

### Final Answer
The fractions \( \frac{2}{6} \) and \( \frac{14}{42} \) are equivalent.

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