Find if the given fractions are equivalent:
`60/(75), 68/(85)`

Answer

To determine if the fractions \( \frac{60}{75} \) and \( \frac{68}{85} \) are equivalent, we can simplify both fractions and see if they reduce to the same value.

### Step 1: Simplify \( \frac{60}{75} \)

1. Find the greatest common divisor (GCD) of 60 and 75.
- The factors of 60 are: \( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \)
- The factors of 75 are: \( 1, 3, 5, 15, 25, 75 \)
- The GCD is 15.

2. Divide both the numerator and the denominator by the GCD:
\[ \frac{60 \div 15}{75 \div 15} = \frac{4}{5} \]

### Step 2: Simplify \( \frac{68}{85} \)

1. Find the greatest common divisor (GCD) of 68 and 85.
- The factors of 68 are: \( 1, 2, 4, 17, 34, 68 \)
- The factors of 85 are: \( 1, 5, 17, 85 \)
- The GCD is 17.

2. Divide both the numerator and the denominator by the GCD:
\[ \frac{68 \div 17}{85 \div 17} = \frac{4}{5} \]

### Conclusion

Both fractions simplify to \( \frac{4}{5} \). Therefore, the fractions \( \frac{60}{75} \) and \( \frac{68}{85} \) are equivalent.

### Final Answer
Yes, the fractions \( \frac{60}{75} \) and \( \frac{68}{85} \) are equivalent.

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