Drawing an area model involves visually representing multiplication as the area of a rectangle, breaking down the factors into their expanded form (tens, ones, etc.) to simplify the calculation. This helps to understand the distributive property of multiplication.
Here's a step-by-step guide:
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Express Numbers in Expanded Form: Decompose each factor into its place values. For example, if you are multiplying 23 x 19, you would express 23 as 20 + 3, and 19 as 10 + 9.
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Draw a Rectangle: Create a rectangle and divide it into smaller rectangles based on the expanded forms of the factors. For 23 x 19, you would divide the rectangle into four smaller rectangles.
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Label the Sides: Label the sides of the larger rectangle with the expanded forms of the numbers. One side would be labeled '20 + 3', and the adjacent side would be '10 + 9'.
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Calculate the Areas: Find the area of each smaller rectangle by multiplying the corresponding side lengths.
- Rectangle 1: 20 x 10 = 200
- Rectangle 2: 20 x 9 = 180
- Rectangle 3: 3 x 10 = 30
- Rectangle 4: 3 x 9 = 27
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Add the Areas: Sum up the areas of all the smaller rectangles to find the total area, which represents the product of the original two numbers. 200 + 180 + 30 + 27 = 437. Therefore, 23 x 19 = 437.
Example:
Multiplying 23 x 19 using the area model:
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Expanded forms: 23 = 20 + 3, 19 = 10 + 9
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Draw a rectangle divided into four smaller rectangles.
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Label the sides as described above.
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Calculate:
10 9 20 200 180 3 30 27 -
Add: 200 + 180 + 30 + 27 = 437
The area model visually breaks down the multiplication process, making it easier to understand how the distributive property works and simplifying mental calculations.
