How To Use Matrix Models for Multi-Digit Multiplication

A matrix model represents a multiplication equation as place-values along rows and columns within a grid

A matrix model represents a multiplication equation as a grid, with the place-values of the factors along the rows and columns. Each cell in the grid contains a partial product, which is the result of multiplying the corresponding elements from the rows and columns. These partial products are then added together to find the overall product of the multiplication equation.

Matrix models are a more advanced visual aid than area models, which also utilizes grids for multiplication equations; however in area models, each cell represents a single unit, while in matrix models, each cell represents multiple units.

To use a matrix model for multiplication:

  1. Draw a rectangle
  2. Divide the rectangle into rows with the number of rows equaling the number of digits in the first number. For each row, write the value of the digit with the corresponding place value.
  3. Further divide the rectangle into columns with the number of columns equaling the number of digits in the second number. For each column, write the value of the digit with the corresponding place value.
  4. For each cell, multiply the value of the row with the value of the column. The result of that multiplication is a partial product.
  5. Sum up the partial products to calculate the total product of the matrices.

For example, let's consider the multiplication equation 24 x 36:

  1. The first number is 24, which has 2 digits, so divide the rectangle into 2 rows. The tens digit in 24 is 2, so the value of the first row is 20. The ones digit is 4, so the value of the second row is 4.
  2. The second number is 36, which has 2 digits, so divide the rectangle into 2 columns. The tens digit in 36 is 3, so the value of the first column is 30. The ones digit is 6, so the value of the second column is 6.
  3. Determine the partial products by multiplying the values of the rows and columns.
    • 20 x 30 = 600
    • 20 x 6 = 120
    • 4 x 30 = 120
    • 4 x 6 = 24
  4. Add together each of the partial products to determine the total products
    • 600 + 120 + 120 + 24 = 864

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