Find if the given fractions are equivalent:
`84/(96), 65/(72)`

Answer

To determine if the fractions \( \frac{84}{96} \) and \( \frac{65}{72} \) are equivalent, we need to simplify both fractions and see if they reduce to the same value.

### Step 1: Simplify the first fraction \( \frac{84}{96} \)

1. **Find the GCD (Greatest Common Divisor)** of 84 and 96.
- The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- The common factors are: 1, 2, 3, 4, 6, 12
- The GCD is 12.

2. **Divide both the numerator and the denominator by the GCD**:
\[ \frac{84 \div 12}{96 \div 12} = \frac{7}{8} \]

### Step 2: Simplify the second fraction \( \frac{65}{72} \)

1. **Find the GCD of 65 and 72**.
- The factors of 65 are: 1, 5, 13, 65
- The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- The only common factor is: 1
- The GCD is 1.

2. **Divide both the numerator and the denominator by the GCD**:
\[ \frac{65 \div 1}{72 \div 1} = \frac{65}{72} \]

### Step 3: Compare the simplified fractions

Now we have:
- \( \frac{84}{96} \) simplifies to \( \frac{7}{8} \)
- \( \frac{65}{72} \) remains \( \frac{65}{72} \)

Since \( \frac{7}{8} \) is not equal to \( \frac{65}{72} \), the two fractions are **not equivalent**.

### Final Conclusion
The fractions \( \frac{84}{96} \) and \( \frac{65}{72} \) are not equivalent.

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