Fill in the boxes and complete the equivalent fractions:
`16/(21)=80/(square)=square/(189)`

Answer

To solve the problem of finding the equivalent fractions for the equation \( \frac{16}{21} = \frac{80}{\square} = \frac{\square}{189} \), we will follow these steps:

### Step 1: Set up the equations
We know that:
\[ \frac{16}{21} = \frac{80}{x} = \frac{y}{189} \]
where \( x \) and \( y \) are the values we need to find.

### Step 2: Solve for \( x \)
From the first part of the equation, we can set up the equation:
\[ \frac{16}{21} = \frac{80}{x} \]
Cross-multiplying gives us:
\[ 16 \cdot x = 21 \cdot 80 \]
Calculating \( 21 \cdot 80 \):
\[ 21 \cdot 80 = 1680 \]
So we have:
\[ 16x = 1680 \]
Now, divide both sides by 16 to solve for \( x \):
\[ x = \frac{1680}{16} \]
Calculating \( \frac{1680}{16} \):
\[ x = 105 \]

### Step 3: Solve for \( y \)
Now we will use the second part of the equation:
\[ \frac{80}{x} = \frac{y}{189} \]
Substituting \( x = 105 \):
\[ \frac{80}{105} = \frac{y}{189} \]
Cross-multiplying gives us:
\[ 80 \cdot 189 = 105 \cdot y \]
Calculating \( 80 \cdot 189 \):
\[ 80 \cdot 189 = 15120 \]
So we have:
\[ 15120 = 105y \]
Now, divide both sides by 105 to solve for \( y \):
\[ y = \frac{15120}{105} \]
Calculating \( \frac{15120}{105} \):
\[ y = 144 \]

### Final Answer
Thus, the completed equivalent fractions are:
\[ \frac{16}{21} = \frac{80}{105} = \frac{144}{189} \]