Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?
(1 point)
Responses
5(3+7)
5 times open paren 3 plus 7 close paren
(5+3)⋅(5+7)
open paren 5 plus 3 close paren times open paren 5 plus 7 close paren
5⋅3⋅7
5 times 3 times 7
(5⋅3)+(5⋅7)
open paren 5 times 3 close paren plus open paren 5 times 7 close paren
(1 point)
The number sentence that shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together) is:
(5⋅3)+(5⋅7)
This represents the distributive property because it is breaking down the area of the rectangle into two separate parts: the area of the left rectangle (5⋅3) and the area of the right rectangle (5⋅7). By adding these two separate areas together, we get the total area of the entire rectangle.
To represent the area of the entire rectangle using the distributive property, we need to find the sum of the areas of the two smaller rectangles. The distributive property states that for any numbers a, b, and c, (a + b) * c is equal to a * c + b * c.
In this case, we have two smaller rectangles with dimensions 5 and 3, and 5 and 7.
The correct number sentence that represents the area of the entire rectangle using the distributive property is:
(5 * 3) + (5 * 7)
This is because we can break down the total area into the sum of the areas of the two smaller rectangles. The first term (5 * 3) represents the area of the rectangle with dimensions 5 and 3, and the second term (5 * 7) represents the area of the rectangle with dimensions 5 and 7. By adding these two areas together, we get the total area of the entire rectangle.