if the mix ration for a certain chemical is 1:8 when it is mixed with water (chemical:water), how many gallons of water would be mixed with $\frac{1}{2}$ gallon of chemical?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Proportional Reasoning" ], "new_concepts": [], "current_concepts": [ "Proportional Reasoning", "Ratio Representation" ] } ## Set up the proportion based on the given ratio $$ \frac{\text{chemical}}{\text{water}} = \frac{1}{8} $$ ## Substitute the given chemical amount and solve for water $$ \begin{aligned} \frac{\frac{1}{2}}{x} &= \frac{1}{8} \ x &= 8 \cdot \frac{1}{2} \ x &= 4 \end{aligned} $$ 4 gallons { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Proportional Reasoning" ] }

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Explanation:

Set up the proportion based on the given ratio

Substitute the given chemical amount and solve for water

Answer: