Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?
A (5 X 3) + (5 X 7)
B 5(3+7)
C 5X3X7
D (5+3) X (5+7)
The correct answer is A (5 X 3) + (5 X 7).
The distributive property states that for any numbers a, b, and c, the expression a(b + c) is equal to ab + ac. In this case, we want to represent the area of the entire rectangle by using the distributive property.
Option A (5 X 3) + (5 X 7) represents the area of the two separate rectangles being added together, but it does not use the distributive property.
Option B 5(3+7) represents the distributive property, where the number 5 is being multiplied by the sum of 3 and 7. This simplifies to 5(10), which is equal to 50, representing the area of the entire rectangle.
Option C 5X3X7 does not use the distributive property. It simply multiplies the three numbers together.
Option D (5+3) X (5+7) also does not use the distributive property, as it is multiplying two separate sums together.
Therefore, the correct answer is B, 5(3+7).
To use the distributive property to represent the area of the entire rectangle, we need to break down the rectangle into two smaller rectangles and then add their areas together.
Let's analyze the options:
A) (5 X 3) + (5 X 7): This equation represents finding the area of two separate rectangles, one with dimensions 5x3 and the other with dimensions 5x7. This is the correct use of the distributive property because we are adding the areas of the two rectangles together.
B) 5(3+7): This equation represents finding the area of a single rectangle with dimensions 5x(3+7). This is not an example of using the distributive property because we are only multiplying the length by the sum of the widths, but not breaking the rectangle into smaller parts.
C) 5X3X7: This equation represents finding the area of a single rectangle with dimensions 5x3x7. This is not an example of using the distributive property as we do not see the addition of areas.
D) (5+3) X (5+7): This equation represents finding the area of a single rectangle with dimensions (5+3) x (5+7). This is not an example of using the distributive property as we see the multiplication of the length and width, but not the addition of areas.
Therefore, the correct number sentence that shows how the distributive property can be used to represent the area of the entire rectangle is A) (5 X 3) + (5 X 7).