On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the least possible distance between any two of the tick marks?

Step-by-step explanation:

Total number length should be divisible by 5 and 7, simply take the LCM of both numbers. i.e 35

so the total distance is 35

the large marks will be at: 7, 14, 21, 28, 35

the small marks will be at: 5, 10, 15, 20, 25, 30, 35

least distance is 1 (between 14 & 15 and between 20 & 21).

therefore,

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Step-by-step explanation: