PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
9
Explanation
The phrase 'from 1 to 7' implies an interval length. The total distance between 1 and 7 is \( 7 - 1 = 6 \). To find out how many times a step of \( \frac{7}{11} \) can fit into this interval, we divide the interval length by the fraction: \( 6 \div \frac{7}{11} = 6 \times \frac{11}{7} = \frac{66}{7} = 9.42 \). Thus, the full fraction occurs exactly 9 times within this range.
Key Points
- > Interval distance = Final value - Initial value = 7 - 1 = 6.
- > Number of occurrences = Interval length \( \div \) Fraction step.
- > Calculation: \( 6 \div (\frac{7}{11}) = \frac{66}{7} \).
- > \( \frac{66}{7} \) equals \( 9\frac{3}{7} \) or 9.42.
- > The full step occurs 9 whole times.
- > If the question asked 'how many times in 7', it would be \( 7 \div (\frac{7}{11}) = 11 \).
- > The phrasing 'from 1 to 7' restricts the available space to 6 units.
Additional Information
Fraction Divisions
| Phrasing | Math Translation | Result |
|---|---|---|
| How many 1/3s in 3? | \( 3 \div \frac{1}{3} \) | 9 times |
| How many 7/11s in 7? | \( 7 \div \frac{7}{11} \) | 11 times |
| How many 7/11s from 1 to 7? | \( (7-1) \div \frac{7}{11} \) | 9 times |
Memory Tips
- Interval Logic: 'From X to Y' always implies a distance of (Y - X). Always subtract first before dividing.