Find if the given fractions are equivalent:
`58/(75), 42/(55)`

Answer

To determine if the fractions \( \frac{58}{75} \) and \( \frac{42}{55} \) are equivalent, we can follow these steps:

### Step 1: Understand the concept of equivalent fractions
Two fractions are equivalent if they represent the same value when simplified or if their cross-products are equal.

### Step 2: Cross-multiply the fractions
To check if the fractions are equivalent, we can cross-multiply:
- Multiply the numerator of the first fraction by the denominator of the second fraction.
- Multiply the numerator of the second fraction by the denominator of the first fraction.

So, we calculate:
\[ 58 \times 55 \quad \text{and} \quad 42 \times 75 \]

### Step 3: Calculate the cross-products
Now, let's calculate each product:
1. \( 58 \times 55 = 3190 \)
2. \( 42 \times 75 = 3150 \)

### Step 4: Compare the cross-products
Now, we compare the two products:
- \( 3190 \) (from \( 58 \times 55 \))
- \( 3150 \) (from \( 42 \times 75 \))

Since \( 3190 \neq 3150 \), the fractions are not equivalent.

### Conclusion
The fractions \( \frac{58}{75} \) and \( \frac{42}{55} \) are not equivalent.

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