Dexter read 11 science fiction books and 5 history books. Lena read 9 science fiction books and 4 history books. Compare the students’ ratios of science fiction books to history books.

Let's work through the problem step-by-step.

1. 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.

2. Write the ratios as fractions:

   • Dexter: ( \frac{11}{5} )
   • Lena: ( \frac{9}{4} )

3. 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} ]

4. 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.

5. 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} )