. Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?
Let's assume that the length of the larger rectangle is 'a' and the width is 'b'.
The area of the larger rectangle is given by a * b.
Now, let's assume that the lengths of the smaller rectangles are 'c' and 'd', and the widths are 'e' and 'f'.
The area of the smaller rectangles are given by c * e and d * f.
To find the area of the entire rectangle (both rectangles together), we can use the distributive property as follows:
Area of entire rectangle = (a * b) + (c * e + d * f)
This shows how the distributive property can be used to represent the area of the entire rectangle.
To represent the area of the entire rectangle using the distributive property, we can break the rectangle into two smaller rectangles and add their individual areas.
Let's say the length of the rectangle is 'L' and the width is 'W'.
The distributive property states: a × (b + c) = (a × b) + (a × c).
In this case, we can use the distributive property by breaking the length (L) into two parts, such as L = L/2 + L/2.
So, the number sentence representing the area of the entire rectangle using the distributive property would be:
A = (L/2 × W) + (L/2 × W)
or
A = 2 × (L/2 × W)
To use the distributive property to represent the area of the entire rectangle, you need to break down the rectangle into smaller rectangles. Let's assume the entire rectangle is represented by a length of L units and a width of W units. We can split the rectangle into two smaller rectangles, one with a width of X units and the other with a width of (W - X) units.
Using the distributive property, we can represent the area of the entire rectangle as the sum of the areas of the two smaller rectangles:
Area of the entire rectangle = Area of first smaller rectangle + Area of second smaller rectangle
= L * X + L * (W - X)
= LX + LW - LX (using the distributive property to expand L * (W - X))
= LX - LX + LW (combining like terms)
= LW (the two LX terms cancel out)
Therefore, the number sentence that shows how the distributive property can be used to represent the area of the entire rectangle is:
L * X + L * (W - X) = LW