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Step 1:I'll solve this step by step using the specified LaTeX formatting guidelines:
Step 2:: Identify the Greatest Common Factor (GCF)
To simplify the ratio, we need to find the largest number that divides both 120 and 150 evenly.
Step 3:: Find the Factors
- Factors of 120: $$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 40, 60, 120
- Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Step 4:: Determine the Greatest Common Factor
The greatest common factor is $$30$$.
Step 5:: Divide Both Numbers by the GCF
\frac{120}{30} : \frac{150}{30} = 4:5
Final Answer
The simplest form of the ratio 120:150 is 4:5.
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