Fill in the missing numbers:
`4:5 = 32: square = square : 20 = 8: square`

Answer

To solve the problem of filling in the missing numbers in the ratios, we can follow these steps:

### Step 1: Understand the Ratios
We have the ratios given as:
- \( 4:5 = 32: \square = \square : 20 = 8: \square \)

### Step 2: Set Up the Ratios
We can express the ratios in fraction form:
- \( \frac{4}{5} = \frac{32}{x} \)
- \( \frac{x}{20} = \frac{8}{y} \)

### Step 3: Solve for the First Missing Number (x)
From the first part \( \frac{4}{5} = \frac{32}{x} \):
- Cross-multiply to find \( x \):
\[ 4x = 5 \times 32 \]
\[ 4x = 160 \]
\[ x = \frac{160}{4} = 40 \]

### Step 4: Solve for the Second Missing Number (y)
Now we have \( x = 40 \). We can use this in the second part \( \frac{x}{20} = \frac{8}{y} \):
- Substitute \( x \) into the equation:
\[ \frac{40}{20} = \frac{8}{y} \]
- Cross-multiply:
\[ 40y = 20 \times 8 \]
\[ 40y = 160 \]
\[ y = \frac{160}{40} = 4 \]

### Step 5: Fill in the Missing Numbers
Now we can fill in the missing numbers:
- The completed ratios are:
\[ 4:5 = 32:40 = 16:20 = 8:10 \]

### Final Answer
The missing numbers are:
- First missing number: **40**
- Second missing number: **4**

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