Find if the given fractions are equivalent:
`36/(252), 12/(84)`

Answer

To determine if the fractions \( \frac{36}{252} \) and \( \frac{12}{84} \) are equivalent, we will simplify both fractions and see if they reduce to the same value.

### Step 1: Simplify \( \frac{36}{252} \)

To simplify \( \frac{36}{252} \), we need to find the greatest common divisor (GCD) of 36 and 252.

- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
- The factors of 252 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

The GCD of 36 and 252 is 36.

Now, divide both the numerator and the denominator by their GCD:

\[ \frac{36 \div 36}{252 \div 36} = \frac{1}{7} \]

### Step 2: Simplify \( \frac{12}{84} \)

Next, we simplify \( \frac{12}{84} \) by finding the GCD of 12 and 84.

- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The GCD of 12 and 84 is 12.

Now, divide both the numerator and the denominator by their GCD:

\[ \frac{12 \div 12}{84 \div 12} = \frac{1}{7} \]

### Conclusion

Both fractions simplify to \( \frac{1}{7} \). Therefore, \( \frac{36}{252} \) and \( \frac{12}{84} \) are equivalent fractions.

### Final Answer

Yes, the fractions \( \frac{36}{252} \) and \( \frac{12}{84} \) are equivalent.

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