How to Use Area Models and the Distributive Property to Multiply?

Multiplying using area models and the distributive property is a visual and conceptual way to understand multiplication.

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A Step-by-step Guide to Use Area Models and the Distributive Property to Multiply

Here are the steps to use these methods:

Step 1: Understand the Area Model:

An area model is a rectangle that represents the two numbers being multiplied. The length of the rectangle represents one factor, and the width represents the other. The area of the rectangle represents the product.

Step 2: Break down the Numbers:

To use the distributive property, you need to break down the numbers into smaller parts.

Step 3: Use the Distributive Property:

Once you have broken down the numbers, you can use the distributive property to multiply.

Step 4: Draw the Area Model:

To use the area model, draw a rectangle with the length and width representing the two factors. Then divide the rectangle into smaller rectangles to match the parts from the distributive property.

Step 5: Multiply and Add:

Finally, multiply each part separately and then add the products together to get the final product.

Using Area Models and the Distributive Property to Multiply – Example 1:

Use the area model to multiply \(24 × 4\).

Solution:

Step 1: Break down the numbers: \(24 = 20 + 4\) Step 2: Use the distributive property: \(24 × 4 = (20 × 4) + (4 × 4)\) Step 3: Draw the area model with smaller rectangles: Step 4: Multiply and add: \(20 × 4 = 80\) \(4 × 4 = 16\) \(80 + 16 = 96\) Therefore, \(24 × 4 = 96\).