There is a paper tape 1 m in length.
After marking the points where this tape is divided into three equal parts , five equal parts and seven equal parts, respectively, this tape is cut off at the point marked.
Find all the kinds of length of the tape after cutting.
After marking the points where this tape is divided into three equal parts , five equal parts and seven equal parts, respectively, this tape is cut off at the point marked.
Find all the kinds of length of the tape after cutting.
Answer
1/7 m, 2/35 m, 3/35 m, 1/21 m, 1/15 m, 1/35 m
Solution
It is hard to compare the size of fractions in Fig. 1.
Then, the length of a paper tape is set to 105 which is the least common multiple of 3, 5 and 7 and cutting part is expressed as shown in Fig.2.
If this is made into the number straight line, it will become as it is shown in Fig. 3.
Then, the length of a paper tape is set to 105 which is the least common multiple of 3, 5 and 7 and cutting part is expressed as shown in Fig.2.
If this is made into the number straight line, it will become as it is shown in Fig. 3.
The length of a between is investigated, it is 15 - 0 = 15, 21 - 15 = 6, 30 - 21 = 9, 35 - 30 = 5, 42 - 35 = 7, 45 - 42 = 3.
It turns out that there are six kinds of length.
Therefore, actual length is 15/105= 1/7 m, 6/105 = 2/35 m, 9/105 = 3/35 m, 5/105 = 1/21 m, 7/105 = 1/15 m, and 3/105 = 1/35 m.
