Find if the given fractions are equivalent:
`17/(26), 27/(39)`

Answer

To determine if the fractions \( \frac{17}{26} \) and \( \frac{27}{39} \) are equivalent, we can follow these steps:

### Step 1: Simplify each fraction
We will simplify both fractions to see if they are equal.

**For \( \frac{27}{39} \)**:
- Find the greatest common divisor (GCD) of 27 and 39.
- The GCD of 27 and 39 is 3.
- Divide both the numerator and the denominator by their GCD:
\[ \frac{27 \div 3}{39 \div 3} = \frac{9}{13} \]

**For \( \frac{17}{26} \)**:
- Check if 17 and 26 have any common factors. The only common factor is 1 since 17 is a prime number.
- Therefore, \( \frac{17}{26} \) is already in its simplest form.

### Step 2: Compare the simplified fractions
Now we compare the simplified fractions:
- \( \frac{17}{26} \) remains \( \frac{17}{26} \).
- \( \frac{27}{39} \) simplifies to \( \frac{9}{13} \).

### Step 3: Check if the fractions are equal
Now we need to check if \( \frac{17}{26} \) is equal to \( \frac{9}{13} \).

To check if two fractions are equivalent, we can cross-multiply:
\[ 17 \times 13 \quad \text{and} \quad 9 \times 26 \]
Calculating both:
- \( 17 \times 13 = 221 \)
- \( 9 \times 26 = 234 \)

Since \( 221 \neq 234 \), the fractions are not equivalent.

### Conclusion
The fractions \( \frac{17}{26} \) and \( \frac{27}{39} \) are not equivalent.

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