Question

Enter the missing values in the area model to find 5(2t + 4)

| 2t | ___
---------------
5 |____ | +20

Answer 1

Enter the missing values in the area model to find 5(2t + 4)

| 2t | ___
---------------
5 |____ | +20

According to the model above 5(2t + 4)

Answer 2

Enter the missing values in the area model to find 6(6m - 4)

| ___ | -4
---------------
6 |36m | ___

According to the model above 6(6m - 4)=

Answer 3

Enter the missing values in the area model to find 3(4v -9)

| ___ | -9
---------------
3 |12v| ___

According to the model above 3(4v - 9)=

Answer 4

Enter the missing values in the area model to find 7(7p - 7)

| ___ | -7
---------------
7 |49p| ___

According to the model above 7(7p - 7)

Answer 5

To solve the area model for the expression \( 5(2t + 4) \), we can break it down into parts.

First, let's recognize that the expression \( 2t + 4 \) can be split into two terms:

- \( 2t \)
- \( 4 \)

Now we can fill in the area model. The area model consists of a rectangle divided into two parts:

- One part along the top is labeled \( 2t \) (the width).
- The other part alongside it is labeled \( 4 \) (the width).

On the left side (the height), we have \( 5 \) for both sections since we are multiplying everything by \( 5 \).

Let's calculate the areas of both sections:

- For the section corresponding to \( 2t \):
\[
\text{Area} = \text{Height} \times \text{Width} = 5 \times 2t = 10t
\]

- For the section corresponding to \( 4 \):
\[
\text{Area} = \text{Height} \times \text{Width} = 5 \times 4 = 20
\]

Thus, the completed area model will look like this:

\[
\begin{array}{|c|c|}
\hline
2t & 4 \\
\hline
5 & 10t & + 20 \\
\hline
\end{array}
\]

So, the missing values are \( 10t \) in the bottom left cell and \( 4 \) in the top right cell. The full model is:

| 2t | 4 |
----------------
| 5 | 10t | +20 |

This confirms that \( 5(2t + 4) = 10t + 20 \).

Answer 6

To fill out the area model for finding \( 5(2t + 4) \), we can break it into its components and represent them in the model.

We start with the expression:

\[
5(2t + 4)
\]

This expression can be expanded using the distributive property:

\[
5 \times 2t + 5 \times 4 = 10t + 20
\]

Now we fill in the area model:

1. The top-left cell represents \( 2t \) (one part of the expression).
2. The top-right cell is the missing value we need to find, which represents the \( 4 \) in \( 5(2t + 4) \).
3. The left side represents the height, which is \( 5 \).

Now we calculate the missing values:

- The area corresponding to \( 2t \) is:
\[
5 \times 2t = 10t
\]

So we fill in the bottom-left cell with \( 10t \).

- For the area corresponding to \( 4 \):
\[
5 \times 4 = 20
\]

Thus, we fill in the bottom-right cell with \( 20 \).

Now, we can present the completed area model:

| 2t | 4 |
|---|---|
| 5 | 10t | +20 |

In summary, the completed area model reveals:

- The missing value in the top-right cell is \( 4 \).
- The missing value in the bottom-left cell is \( 10t \).

This results in the final model:

| 2t | 4 |
|---|---|
| 5 | 10t | +20 |

So the complete expression represented in the area model confirms that \( 5(2t + 4) = 10t + 20 \).

Answer 7

To fill in the missing values in the area model for the expression \( 6(6m - 4) \), we can break it down using the distributive property.

Given the expression:

\[
6(6m - 4)
\]

We can expand this:

\[
6 \times 6m + 6 \times (-4) = 36m - 24
\]

Now, we can fill in the area model.

1. The top-left cell corresponds to the term \( 6m \) (the first part of the expression). Since it’s not specified, we can denote this as \( 6m \).
2. The top-right cell corresponds to the term \(-4\) and is already provided.
3. The height of the model (the leftmost value) is \( 6 \).
4. The bottom-left cell should represent the area of \( 6 \times 6m = 36m\) which is already provided.
5. The bottom-right cell is the missing value we need to calculate, which corresponds to the area for the term \( -4 \).

### Calculating the bottom-right cell:

The area for \(-4\) would be:

\[
6 \times (-4) = -24
\]

Now we can fill in all the cells of the area model:

| 6m | -4 |
|---|-----|
| 6 | 36m | -24 |

### Therefore:

According to the model above, we have:

\[
6(6m - 4) = 36m - 24
\]

The completed model now shows the correct values.

Answer 8

To fill in the missing values in the area model for the expression \( 3(4v - 9) \), we can expand it using the distributive property.

Given the expression:

\[
3(4v - 9)
\]

We can expand this:

\[
3 \times 4v + 3 \times (-9) = 12v - 27
\]

Now, we can fill in the area model.

1. The top-left cell corresponds to the term \( 4v \) (the first part of the expression).
2. The top-right cell corresponds to the given term \( -9 \).
3. The height of the model (the leftmost value) is \( 3 \).
4. The bottom-left cell represents the value for \( 3 \times 4v = 12v \), which is already provided.
5. The bottom-right cell should correspond to the area for the term \( -9 \).

### Calculating the bottom-right cell:

The area for \( -9 \) would be:

\[
3 \times (-9) = -27
\]

Now we can fill in all the cells of the area model:

| 4v | -9 |
|---|-----|
| 3 | 12v | -27 |

### Therefore:

According to the model above,

\[
3(4v - 9) = 12v - 27
\]

So the completed model now shows all the correct values.

Answer 9

To fill in the missing values in the area model for the expression \( 7(7p - 7) \), we can expand it using the distributive property.

Given the expression:

\[
7(7p - 7)
\]

We can expand this expression:

\[
7 \times 7p + 7 \times (-7) = 49p - 49
\]

Now we can fill in the area model accordingly.

1. The top-left cell corresponds to the term \( 7p \) (the first part of the expression).
2. The top-right cell corresponds to the term \(-7\) (which is already given).
3. The height of the model (the leftmost value) is \( 7 \).
4. The bottom-left cell represents the value for \( 7 \times 7p = 49p\), which is already provided.
5. The bottom-right cell corresponds to the area for the term \( -7 \).

### Calculating the bottom-right cell:

The area for \(-7\) would be:

\[
7 \times (-7) = -49
\]

Now we can fill in all the cells of the area model:

| 7p | -7 |
|---|-----|
| 7 | 49p | -49 |

### Therefore:

According to the model above,

\[
7(7p - 7) = 49p - 49
\]

So the completed model now shows all the correct values.