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Enter the missing values in the area model to find 8(9f + 2)

1#____. -2
8 72f. 2#____

3 answers

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: \[ 72f + 16 \]

  1. 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.
According to the model above 8(9f - 2) =

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

  1. 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, \(8(9f - 2) = 72f - 16\).