Let's work through the problem step-by-step.
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Determine the ratios’ form:
- Dexter's ratio of science fiction books to history books: 11 science fiction books to 5 history books.
- Lena's ratio of science fiction books to history books: 9 science fiction books to 4 history books.
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Write the ratios as fractions:
- Dexter: \( \frac{11}{5} \)
- Lena: \( \frac{9}{4} \)
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Rewrite with a common denominator:
The least common denominator (LCD) of 5 and 4 is 20. We will convert both fractions to have a denominator of 20.- For Dexter: \[ \frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20} \]
- For Lena: \[ \frac{9}{4} = \frac{9 \times 5}{4 \times 5} = \frac{45}{20} \]
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Compare:
Now, we can compare the two fractions:- Dexter's ratio: \( \frac{44}{20} \)
- Lena's ratio: \( \frac{45}{20} \)
Since \( \frac{44}{20} < \frac{45}{20} \), we can conclude that Lena has a higher ratio of science fiction books to history books compared to Dexter.
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Answer the question:
Based on the comparisons we made, the correct option is:
- \( \frac{44}{20} < \frac{45}{20} \)
So, the correct comparison of the ratios for this problem is:
- \( \frac{44}{20} < \frac{45}{20} \)
8 answers