the model shows the expression $20 + 16$.

which expression is equivalent to this sum?

- $4(5) + 4$
- $4 + 5 + 4$
- $4(5 + 4)$
- $5(4 + 4)$

Question

the model shows the expression $20 + 16$.

which expression is equivalent to this sum?

- $4(5) + 4$
- $4 + 5 + 4$
- $4(5 + 4)$
- $5(4 + 4)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Distributive Property", "Area Model" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Distributive Property", "Area Model", "Equivalent Expressions" ] } ## Analyze the area model dimensions Using the **Area Model** knowledge point $$ \begin{aligned} &\text{Total height} = 4\text{ units}\ &\text{Yellow width} = 5\text{ units} \implies \text{Yellow area} = 4 \times 5 = 20\ &\text{Purple width} = 4\text{ units} \implies \text{Purple area} = 4 \times 4 = 16 \end{aligned} $$ ## Find the greatest common factor Using the **Greatest Common Factor** knowledge point $$ \begin{aligned} &\text{Factors of } 20: 1, 2, 4, 5, 10, 20\ &\text{Factors of } 16: 1, 2, 4, 8, 16\ &\text{GCF}(20, 16) = 4 \end{aligned} $$ ## Apply the distributive property Using the **Distributive Property** and **Equivalent Expressions** knowledge points $$ \begin{aligned} 20 + 16 &= 4 \times 5 + 4 \times 4\ &= 4(5 + 4) \end{aligned} $$

(A) $4(5) + 4$

(B) $4 + 5 + 4$

(C) $4(5 + 4)$

(D) $5(4 + 4)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Distributive Property" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the area model dimensions

Find the greatest common factor

Apply the distributive property

Answer: