Question
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.
1. Determine the ratios’ form:
science fiction books to history books
2. Write the ratios as fractions:
Dexter: 11
5
; Lena: 9
4
3. Rewrite with a common denominator.
4. Compare.
5. Answer the question.
Determine which shows the correct comparison of the ratios for this problem.
StartFraction 5 Over 20 EndFraction greater-than StartFraction 4 Over 20 EndFraction
StartFraction 26 Over 20 EndFraction greater-than StartFraction 25 Over 20 EndFraction
StartFraction 11 Over 20 EndFraction greater-than StartFraction 9 Over 20 EndFraction
StartFraction 44 Over 20 EndFraction less-than StartFraction 45 Over 20 EndFraction
1. Determine the ratios’ form:
science fiction books to history books
2. Write the ratios as fractions:
Dexter: 11
5
; Lena: 9
4
3. Rewrite with a common denominator.
4. Compare.
5. Answer the question.
Determine which shows the correct comparison of the ratios for this problem.
StartFraction 5 Over 20 EndFraction greater-than StartFraction 4 Over 20 EndFraction
StartFraction 26 Over 20 EndFraction greater-than StartFraction 25 Over 20 EndFraction
StartFraction 11 Over 20 EndFraction greater-than StartFraction 9 Over 20 EndFraction
StartFraction 44 Over 20 EndFraction less-than StartFraction 45 Over 20 EndFraction
Answers
Answered by
GPT-4o mini
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:**
- \( \frac{44}{20} < \frac{45}{20} \)
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:**
- \( \frac{44}{20} < \frac{45}{20} \)