Question

complete the explanation of how the figure illustrates that 6(9) = 6(6) + 6(3).
the area is the product of the length and width (6 × \square). it is also the sum of the areas of the rectangles separated by the dished line (6 × \square and 6 × 3). so, 6(9) = 6(6) + 6(3).

Explanation:

Step1: Analyze the first blank

The equation given is \(6(9)=6(6)+6(3)\), and the area of the whole rectangle is length times width. The length here is related to 9 (since \(6\times9\) is the total area), so the first blank should be 9 because the product is \(6\times9\).

Step2: Analyze the second blank

The two smaller rectangles have areas \(6\times\) [first small length] and \(6\times3\). From the equation \(6(9)=6(6)+6(3)\), we know that one of the smaller rectangles has a length of 6 (since \(6\times6\) is part of the sum), so the second blank is 6.

Answer:

First blank: 9, Second blank: 6