Question

Enter the missing values in the area model to find 8(9f + 2)
1#____. -2
8 72f. 2#____

Answer 1

According to the model above 8(9f - 2) =

Answer 2

To fill in the missing values in the area model for the expression \( 8(9f + 2) \), we can start by rewriting the expression so that it can be broken down into the area model.

1. Distribute the 8 into the terms in the parentheses:

\[
8(9f + 2) = 8 \cdot 9f + 8 \cdot 2
\]

This gives us:
\[
72f + 16
\]

2. Now, in the area model we can visualize it as follows:

```
| 9f | 2
---------------
8 | 72f | 16
```

From this structure:
- The value in the lower left corner corresponds to \( 8 \cdot 9f = 72f \).
- The value in the lower right corner corresponds to \( 8 \cdot 2 = 16 \).
- The value at the upper right corner, which is represented as ??, corresponds to \( 2 \cdot 9f \), which gives us \( 18f \).
- The value at the upper left corner corresponds to \( 2 \), which is already provided.

So now we can fill in the missing values:

1. The value for the area for \( 2 \cdot 9f \) is \( \mathbf{18f} \).
2. The value in the lower left represents \( \mathbf{16} \) as already stated.

Thus, the filled area model should look like this:

```
| 9f | 2
---------------
8 | 72f | 16
---------------
18f | _______ | _
```

Therefore:
1# = \( 18f \)
2# = \( 16 \)

So the completed area model would be:

```
| 9f | 2
---------------
8 | 72f | 16
```

- The missing values filled in are \( 18f \) for the left-hand cell and \( 16 \) for the lower right cell.

Answer 3

To find the expression \(8(9f - 2)\) using an area model, we can follow a similar approach as before, structuring the expression into its components.

1. First, distribute the 8 into the terms in the parentheses:

\[
8(9f - 2) = 8 \cdot 9f + 8 \cdot (-2)
\]

This yields:
\[
8 \cdot 9f - 8 \cdot 2 = 72f - 16
\]

2. To visualize this in an area model, we can lay it out like this:

```
| 9f | -2
-----------------
8 | 72f | -16
```

In this model:
- The upper left cell represents \(8 \cdot 9f = 72f\).
- The upper right cell represents \(8 \cdot (-2) = -16\) (which is negative).

So, the completed expression in terms of area becomes:

\[
8(9f - 2) = 72f - 16
\]

Therefore, \(8(9f - 2) = 72f - 16\).