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Step 1:I'll solve this step-by-step using the specified LaTeX formatting guidelines:
Step 2:: Identify the original ratio
The given ratio is $$4:6
Step 3:: Find the Greatest Common Factor (GCF)
To simplify the ratio, we need to find the largest number that divides both 4 and 6. - Factors of 4: 1, 2, 4 - Factors of 6: 1, 2, 3, 6 - The Greatest Common Factor is 2
Step 4:: Divide both numbers by the GCF
\frac{4}{2} : \frac{6}{2} = 2:3
Final Answer
Key Insights: - Simplifying a ratio means reducing it to the smallest whole numbers that maintain the same proportional relationship - Always divide both numbers by their greatest common factor - The simplified ratio preserves the original proportion
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