Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?
The diagram is a rectangle made of 2 squares, one being larger than the other, they both have the height of 9, one has the length of 6, the other has 11 as the length.
The distributive property states that a(b + c) = ab + ac. In this case, we can represent the area of the entire rectangle by adding the areas of the two smaller rectangles.
The area of the larger rectangle with length 11 and height 9 is 11*9 = 99.
The area of the smaller rectangle with length 6 and height 9 is 6*9 = 54.
Therefore, the number sentence that represents the area of the entire rectangle is 99 + 54.
To find the area of the entire rectangle using the distributive property, you can represent it as the sum of the areas of the individual squares. Let's say A represents the area of the larger square and B represents the area of the smaller square.
The area of the larger square is given by A = length * height, which in this case is A = 11 * 9.
The area of the smaller square is given by B = length * height, which in this case is B = 6 * 9.
Using the distributive property, we can express the area of the entire rectangle as A + B.
So, the number sentence that shows how the distributive property can be used to represent the area of the entire rectangle is:
Area of entire rectangle = A + B = (11 * 9) + (6 * 9)
To represent the area of the entire rectangle using the distributive property, you can break the rectangle into two separate sections (rectangles) and then find the sum of their areas.
Let's denote the larger rectangle with length 11 and height 9, and the smaller rectangle with length 6 and height 9.
The distributive property states that for any numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b, and a and c.
In this case, the larger rectangle can be represented as 11 * 9, and the smaller rectangle as 6 * 9. We can use the distributive property to express the total area of the rectangle as the sum of these two products:
Total Area = (11 * 9) + (6 * 9)
Now we can calculate the answer:
Total Area = 99 + 54
Total Area = 153
Therefore, the number sentence that shows how the distributive property can be used to represent the area of the entire rectangle is:
Total Area = (11 * 9) + (6 * 9)
Total Area = 153