To determine who has a pattern of equivalent ratios for \( \frac{3}{8} \), let's analyze the methods used by Ali and Felicia.
Ali's Method:
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Extend the table to column 16:
- The equivalent ratios for \( \frac{3}{8} \) can be generated by finding ratios in the form of \( \frac{3n}{8n} \) for any integer \( n \). Since \( 8 \) can be extended to \( 16 \) (by using \( n = 2 \)), Ali can form a ratio \( \frac{3}{8} = \frac{6}{16} \).
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Pick a row and write a ratio comparing a number in column 6 to a number in column 16:
- For example, using \( 6 \) (from column 6) and \( 16 \) (from column 16), the ratio \( \frac{6}{16} \) is equivalent to \( \frac{3}{8} \).
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Pick a different row:
- He could again use \( 12 \) from column 6 with \( 32 \) from column 16 to get \( \frac{12}{32} \), which is also equivalent to \( \frac{3}{8} \).
Felicia's Method:
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Extend the table to column 24:
- Extending to 24 allows \( 8 \) to be considered in a multiplication of \( n = 3 \) (as in \( 8 \times 3 = 24 \)). Therefore, \( \frac{3}{8} = \frac{9}{24} \).
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Pick a row and write a ratio comparing a number in column 9 to a number in column 24:
- Using \( 9 \) from column 9 and \( 24 \) from column 24 gives \( \frac{9}{24} \), which is equivalent to \( \frac{3}{8} \).
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Pick a different row:
- Felicia can take \( 18 \) from column 9 and use \( 48 \) from column 24 to form \( \frac{18}{48} \), which is also \( \frac{3}{8} \).
Conclusion:
Both Ali and Felicia are able to correctly form equivalent ratios for \( \frac{3}{8} \) using their respective methods. Therefore, the answer is:
both Ali and Felicia.
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