Use the diagram to answer the question. Which number sentence shows how the distributive property can be used to represent the area of the blue rectangle? Responses A (9 + 6) × (9 + 11)(9 + 6) × (9 + 11) B (9 × 6) + (9 × 11)(9 × 6) + (9 × 11) C 11(6 + 9)11(6 + 9) D 9 × 6 × 11
The diagram is not provided, so it is not possible to determine which number sentence shows how the distributive property can be used to represent the area of the blue rectangle.
The diagram is a rectangle. The height is 9 and one side is split into a long rectangle VERTICALLY and that is 6. The other half is 11.
Based on the given information, the blue rectangle can be represented as the product of the height (9) and the sum of the lengths of the two parts of the side (6 + 11). Therefore, the correct number sentence to represent the area of the blue rectangle using the distributive property is:
C) 11(6 + 9)
To answer this question, we need to understand the distributive property and how it applies to the diagram. The distributive property states that when we multiply a sum by a number, we can distribute the multiplication to each term inside the parentheses.
Let's analyze the diagram to find the dimensions of the blue rectangle:
+-----+-------------------+
| | |
| | |
+-----+---------+ |
| | | 6 |
| | | |
| | +---------+
| | | 9 |
+-----+---------+----+----+
| 9 |
The rectangle has a length of 9 units and a width of 6 units. The diagram also shows that there is an additional rectangle with dimensions 9 units by 11 units.
Now, let's look at the number sentences provided:
A) (9 + 6) × (9 + 11)
B) (9 × 6) + (9 × 11)
C) 11(6 + 9)
D) 9 × 6 × 11
We can eliminate options B) and D) because they do not use the distributive property. They either multiply the dimensions directly or multiply them together without distributing.
The correct answer is either A) or C). To determine the correct choice, let's apply the distributive property to each option:
A) (9 + 6) × (9 + 11) = 9 × 9 + 9 × 11 + 6 × 9 + 6 × 11
C) 11(6 + 9) = 11 × 6 + 11 × 9
By expanding both expressions, we see that Option A) represents the area of the blue rectangle correctly using the distributive property:
9 × 9 + 9 × 11 + 6 × 9 + 6 × 11
Therefore, the correct number sentence that represents the area of the blue rectangle using the distributive property is option A) (9 + 6) × (9 + 11).