Find the fraction equivalent to `35/42` having denominator 30.

Options

A. `25/30`
B. `30/25`
C. `35/30`
D. `42/30`

Answer

To find the fraction equivalent to \( \frac{35}{42} \) with a denominator of 30, we can follow these steps:

### Step 1: Simplify the given fraction
First, we simplify the fraction \( \frac{35}{42} \).

To simplify, we find the greatest common divisor (GCD) of 35 and 42.

- The factors of 35 are: 1, 5, 7, 35
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The GCD is 7.

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

\[ \frac{35 \div 7}{42 \div 7} = \frac{5}{6} \]

### Step 2: Set up the equivalent fraction
Now that we have simplified \( \frac{35}{42} \) to \( \frac{5}{6} \), we want to find an equivalent fraction with a denominator of 30.

### Step 3: Determine the multiplier
To find out what we need to multiply the denominator (6) by to get 30, we calculate:

\[ 30 \div 6 = 5 \]

### Step 4: Multiply the numerator
Since we multiplied the denominator by 5, we must do the same to the numerator:

\[ 5 \times 5 = 25 \]

### Step 5: Write the equivalent fraction
Thus, the equivalent fraction with a denominator of 30 is:

\[ \frac{25}{30} \]

### Conclusion
So, we conclude that:

\[ \frac{35}{42} \text{ is equivalent to } \frac{25}{30} \]