Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (bth rectangles together)?
The distributive property can be used to represent the area of the entire rectangle, by multiplying the sum of the lengths by the sum of the widths of both rectangles.
The number sentence that represents this is:
(A + B) x (C + D)
To represent the area of the entire rectangle using the distributive property, you would multiply the sum of the lengths by the sum of the widths. The number sentence would be:
(A + B) × (C + D) = AC + AD + BC + BD
Where:
- A represents the length of the first rectangle.
- B represents the length of the second rectangle.
- C represents the width of the first rectangle.
- D represents the width of the second rectangle.
This number sentence shows how the distributive property can be used to represent the area of the entire rectangle.
The height is 5 for height for both squares, then the length of one square is 3, then the other one has a length of 7
In that case, if the height of both squares is 5, and one square has a length of 3 while the other square has a length of 7, the number sentence representing the area of the entire rectangle, using the distributive property, would be:
(3 + 7) × (5 + 5) = 10 × 10 = 100
So, the area of the entire rectangle would be 100 square units.
To represent the area of the entire rectangle using the distributive property, we need to break it down into smaller rectangles and then combine their areas. Let's assume the rectangle has a length of L and a width of W. We can divide the rectangle into two smaller rectangles: one with a width of W and a length of L/2, and another with a width of W and a length of L/2.
The area of the first smaller rectangle can be represented as W * (L/2), and the area of the second smaller rectangle can also be represented as W * (L/2). To find the total area of the entire rectangle, we can use the distributive property to combine the areas of the two smaller rectangles:
Total Area = Area of first rectangle + Area of second rectangle
= W * (L/2) + W * (L/2)
Using the distributive property, we can factor out the common term "W":
Total Area = W * (L/2 + L/2)
Simplifying further, we have:
Total Area = W * L
Therefore, the number sentence that shows how the distributive property can be used to represent the area of the entire rectangle is W * L.