Question
10. What is the next fraction in the pattern \( 3 / 8,7 / 8,13 / 8,17 / 8 \)
Ask by Huff Smith. in Kenya
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The next fraction in the pattern is \( \frac{23}{8} \).
Solution
To determine the next fraction in the pattern \( \frac{3}{8}, \frac{7}{8}, \frac{13}{8}, \frac{17}{8} \), let's analyze the numerators:
1. **Current Numerators:** 3, 7, 13, 17
2. **Differences Between Successive Numerators:**
- \( 7 - 3 = 4 \)
- \( 13 - 7 = 6 \)
- \( 17 - 13 = 4 \)
The pattern of differences alternates between **+4** and **+6**.
3. **Predicting the Next Difference:**
- Following the alternation, the next difference should be **+6**.
4. **Calculating the Next Numerator:**
- \( 17 + 6 = 23 \)
5. **Forming the Next Fraction:**
- The denominator remains **8**, so the next fraction is \( \frac{23}{8} \).
**Answer:** \(\boxed{\dfrac{23}{8}}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the next fraction in the pattern, we can first observe the numerators: 3, 7, 13, and 17. The differences between the numerators are as follows: - 7 - 3 = 4 - 13 - 7 = 6 - 17 - 13 = 4 However, there seems to be a cyclical pattern in the differences of 4 and 6. If we assume this pattern continues, we might expect the next difference to be 6 again. Thus, the next numerator would be: 17 + 6 = 23. The denominator remains 8 in all fractions, so the next fraction is \( \frac{23}{8} \).
