Question

which expressions did larry model? check all that apply.

\\(5(7)\\)
\\(30 + 42\\)
\\(6 + (5)(7)\\)
\\(6(5 + 7)\\)
\\((6)(5) + (6)(7)\\)

Explanation:

Analyze the dimensions of the area model

The grid has a height of 6 units.
The width is split into two colored sections:

• A red section with a width of 5 units.
• A blue section with a width of 7 units.

The total width is \(5 + 7 = 12\) units.

Calculate the area of each section

Using the Distributive Property knowledge point:

• The area of the red section is:

$$ 6 \times 5 = 30 $$

• The area of the blue section is:

$$ 6 \times 7 = 42 $$

Express the total area in different forms

Using the Distributive Property knowledge point:

• Sum of individual areas:

$$ (6)(5) + (6)(7) $$

• Simplified sum:

$$ 30 + 42 $$

• Factored form using the height and total width:

$$ 6(5 + 7) $$

Evaluate the given options

Let's check each option against our expressions:

• \(5(7)\): Incorrect.
• \(30 + 42\): Correct.
• \(6 + (5)(7)\): Incorrect.
• \(6(5 + 7)\): Correct.
• \((6)(5) + (6)(7)\): Correct.

Answer:

• 5(7)
• 30 + 42 (Correct answer)
• 6 + (5)(7)
• 6(5 + 7) (Correct answer)
• (6)(5) + (6)(7) (Correct answer)