Drawing a Multiplication Array

1. Understand the Concept: A multiplication array visually represents multiplication problems using rows and columns. For example, to represent \(3 \times 5\), you would create 3 rows with 5 objects (dots, circles, etc.) in each row.
2. Set Up the Array:

• Choose the Numbers: For \(2 \times 7\), you will have 2 rows and 7 columns.
• Draw Rows and Columns: Start by drawing 2 horizontal lines (rows) and then draw 7 vertical lines (columns) to create a grid.
• Fill in the Array: Place a dot or an object in each cell of the grid. For \(2 \times 7\), you will have a total of 14 dots arranged in 2 rows and 7 columns.

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3. Label the Array: You can label the rows and columns to indicate what they represent, such as "Rows = 2" and "Columns = 7".

Drawing a Matrix (Array for Systems of Equations)

1. Write the System of Equations: For example, consider the equations \(2x + y = 18\), \(x + y = 15\), and \(3x - z = 7\).
2. Set Up the Matrix:

• Draw a Square: Create a square or rectangle on your paper.
• Divide into Rows and Columns: For three equations, you will have 3 rows. If you have three variables (x, y, z), you will have 3 columns plus an additional column for the constants on the right side of the equations.
• Fill in the Coefficients: Write the coefficients of each variable in the corresponding cells. For the example above, the first row would have \(2\) (for \(x\)), \(1\) (for \(y\)), and \(0\) (for \(z\)), followed by \(18\) in the last column. Repeat for the other equations.

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3. Label the Matrix: Clearly label each row and column to indicate which equation and variable they correspond to.

Additional Tips

• Use Visual Aids: You can use colored pens or markers to differentiate between rows and columns, making it easier to understand the structure of the array.
• Practice with Examples: Try drawing different arrays with various multiplication problems or systems of equations to become more comfortable with the concept.

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  By following these steps, you can effectively draw both multiplication arrays and matrices to represent mathematical concepts visually. This can enhance understanding and help in solving problems more efficiently.
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