Question

Show how to use the area model and the Distributive Property to find 14×45

Answer 1

To find the product \( 14 \times 45 \) using the area model and the Distributive Property, we can break down each number into more manageable parts.

### Step 1: Break down the numbers
First, let's break down both numbers:
- \( 14 \) can be expressed as \( 10 + 4 \).
- \( 45 \) can be expressed as \( 40 + 5 \).

### Step 2: Set up the area model
Next, we can set up a grid (or area model) based on these breakdowns:

\[
\begin{array}{c|c|c}
& 40 & 5 \\
\hline
10 & 10 \times 40 & 10 \times 5 \\
\hline
4 & 4 \times 40 & 4 \times 5 \\
\end{array}
\]

### Step 3: Calculate the area of each rectangle
Now we will calculate the area of each rectangle in the grid:

- \( 10 \times 40 = 400 \)
- \( 10 \times 5 = 50 \)
- \( 4 \times 40 = 160 \)
- \( 4 \times 5 = 20 \)

### Step 4: Add the areas together
Now, sum all the areas calculated:

\[
400 + 50 + 160 + 20
\]

Calculating that step by step:

1. \( 400 + 50 = 450 \)
2. \( 450 + 160 = 610 \)
3. \( 610 + 20 = 630 \)

Thus, \( 14 \times 45 = 630 \).

### Summary
Using the area model along with the Distributive Property, we find that:

\[
14 \times 45 = 630
\]