What is the smallest fraction that exactly divides 6/7, 5/14, and 10/21_________?
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Answer: A. 30/7
Explanation
Finding the smallest fraction that divides a set of fractions requires dividing the least common multiple. The calculation involves determining the least common multiple of the numerators and greatest common divisor. Executing the fraction division rule simplifies the final mathematical result to thirty over seven. Fractions can be divided by multiplying the dividend by the reciprocal of the divisor fraction. The least common multiple of a set of numbers is the smallest positive integer divisible by all numbers. The greatest common divisor represents the largest positive integer that divides each number without remainder.
Advanced arithmetic operations involving rational numbers require mastering fraction division principles. Engineering calculations frequently handle complex fractional ratios when analyzing gear rotation speeds. Number theory applications utilize least common multiples to synchronize periodic events. Option B suggests thirty over ninety eighths which lacks proper fraction simplification steps. Option C proposes sixty over one forty seventh which uses incorrect numerator and denominator values. Option D offers fifty over two ninety fourths which does not align with the correct arithmetic steps.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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