Fill in the boxes and complete the equivalent fractions:
`32/(42)=384/(square)=square/(546)`

Answer

To solve the problem of finding the equivalent fractions for the equation \( \frac{32}{42} = \frac{384}{\square} = \frac{\square}{546} \), we will fill in the boxes step by step.

### Step 1: Set up the equations
We start with the first part of the equation:
\[ \frac{32}{42} = \frac{384}{x} \]
where \( x \) is the value we need to find.

### Step 2: Cross-multiply
To find \( x \), we can cross-multiply:
\[ 32 \cdot x = 384 \cdot 42 \]

### Step 3: Calculate \( 384 \cdot 42 \)
Now, we calculate \( 384 \cdot 42 \):
\[ 384 \cdot 42 = 16128 \]

### Step 4: Solve for \( x \)
Now we can solve for \( x \):
\[ 32x = 16128 \]
To isolate \( x \), divide both sides by 32:
\[ x = \frac{16128}{32} \]

### Step 5: Perform the division
Now, we perform the division:
\[ x = 504 \]

### Step 6: Set up the second equation
Now we move to the second part of the equation:
\[ \frac{384}{504} = \frac{y}{546} \]
where \( y \) is the value we need to find.

### Step 7: Cross-multiply again
Cross-multiply to find \( y \):
\[ 384 \cdot 546 = 504 \cdot y \]

### Step 8: Calculate \( 384 \cdot 546 \)
Now we calculate \( 384 \cdot 546 \):
\[ 384 \cdot 546 = 209664 \]

### Step 9: Solve for \( y \)
Now we can solve for \( y \):
\[ 504y = 209664 \]
To isolate \( y \), divide both sides by 504:
\[ y = \frac{209664}{504} \]

### Step 10: Perform the division
Now, we perform the division:
\[ y = 416 \]

### Final Result
Thus, the completed equivalent fractions are:
\[ \frac{32}{42} = \frac{384}{504} = \frac{416}{546} \]