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describe the decimal multiplication equation and product shown by the model include details of where each part of the equation is found on the model

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To explain a decimal multiplication equation and its product using a model, let's first define a basic decimal multiplication equation. For example, let’s consider the multiplication of 2.3 and 4.5.

Equation:

\[ 2.3 \times 4.5 = ? \]

Product:

To find the product, we can perform the multiplication: \[ 2.3 \times 4.5 = 10.35 \]

Model Description:

Imagine a model such as a grid or an area model to visually represent this multiplication.

  1. Setting Up the Model:

    • Divide the model into sections based on the whole numbers and decimal parts. For 2.3, you can split it into 2 (whole part) and 0.3 (decimal part). For 4.5, split it into 4 and 0.5.
    • Create a rectangle (or a grid), marking the lengths and widths based on these values where one side is 2.3 and the other side is 4.5.

  2. Creating the Sections:

    • You will have four sections based on the distributive property:
      • \( 2 \times 4 = 8 \)
      • \( 2 \times 0.5 = 1 \)
      • \( 0.3 \times 4 = 1.2 \)
      • \( 0.3 \times 0.5 = 0.15 \)

  3. Calculating Areas:

    • Each of these sections represents a rectangular area.
      • For the section representing \( 2 \times 4 \), the area would be 8.
      • For \( 2 \times 0.5 \), the area will be 1.
      • For \( 0.3 \times 4 \), the area will be 1.2.
      • For \( 0.3 \times 0.5 \), the area will be 0.15.

  4. Combining Areas:

    • To find the total area, you add all these areas together: \[ 8 + 1 + 1.2 + 0.15 = 10.35 \]
    • This total area visually represents the product of \( 2.3 \times 4.5 = 10.35 \).

Summary:

In the model:

  • The equation \( 2.3 \times 4.5 \) is represented by the dimensions of the overall rectangle or grid.
  • Each section of the rectangle corresponds to the respective multiplication parts, leading to their areas that contribute to the final product.
  • The location of each section (top-left, bottom-right, etc.) visually demonstrates how the distributive property works in decimal multiplication.

Understanding this model helps in grasping the concept of multiplying decimals, as it breaks down the process into manageable components while also illustrating the arithmetic visually.