The fox and the weasel have a jumping competition. The fox can jump 412 meters at a time, and the weasel can jump 2/3/4 meters at a time. They only jump once a second. During the competition, set a trap every 12 3/8 meters from the starting point. One of them fell into the trap, and the other jumped a few meters.
This is a practical problem, but through analysis, we know that when a fox (or weasel) falls into a trap for the first time, its jumping distance is an integer multiple of its jumping distance each time, that is, 4 1/2 (or 2 3/4) meters, and it is also an integer multiple of the trap interval 12 3/8 meters. That is, the "least common multiple" of 4 1/2 and 12 3/8 (or the "least common multiple" of 2 3/4 and 12 3/8). In both cases, the problem is basically solved by counting the number of hops to determine who falls into the trap first. The above-mentioned thinking process is essentially to transform a practical problem into a mathematical problem, which is one of the manifestations of mathematical ability. 7. The fox and the weasel have a jumping competition. The fox jumps 6 9/2m each time and the weasel jumps 6 10 each time.
The fox and the weasel have a jumping competition. The fox jumps 6 9/2 meters at a time, and the weasel jumps 6 10/3 meters at a time. They only jump once a second. During the competition, set a trap every 3 2/ 1 m from the starting point. Which of them will jump into the trap first? How many meters did the other one jump when it fell into the trap?