How many fractions are there which cannot be reduced to its lowest numbers among 1/45, 2/45, 3/45 -- 44/45 ?
Answer
Namely, we should find the number which is not the multiple of 3 nor 5 among the numerator from 1 to 44.
Number of the multiple of 3 is 14 by the calculation of 44/3 = 14 remainder 2.
Number of the multiple of 5 is 8 by 44/5 = 8 remainder 4.
Number of the multiple of 15 of the least common multiple of 3 and 5 is 2 by 44/15 = 2 remainder 14.
Therefore, the number of the fractions which cannot be reduced is 44 - (14 + 8 - 2) = 24.
24 fractions
Solution
Since 45= 3 × 3 × 5, it turns out that the fraction of which denominator is 45 can be reduced by the multiple of 3 and 5.Namely, we should find the number which is not the multiple of 3 nor 5 among the numerator from 1 to 44.
Number of the multiple of 3 is 14 by the calculation of 44/3 = 14 remainder 2.
Number of the multiple of 5 is 8 by 44/5 = 8 remainder 4.
Number of the multiple of 15 of the least common multiple of 3 and 5 is 2 by 44/15 = 2 remainder 14.
Therefore, the number of the fractions which cannot be reduced is 44 - (14 + 8 - 2) = 24.
