This way is difficult, but that makes it easy to understand relations between addition and subtraction a little.First, we draw a line and we pick up a point on the line. We make this point 0 (The point where the lines intersect in the figure). Next we take another point on the line and we make this point 1. We make the point 2 which is at twice of length between 0 and 1, from 0 toward 1 (right in the figure). We make the point 3 which is at three times of length between 0 and 1, from 0 toward 1... Similarly we determine the point of every positive integer n. We make the point -1 which is at the same length between 0 and 1, from 0 toward the opposite direction of 1 (left in the figure). We make the point -2 which is at twice of length between 0 and 1, from 0 toward the opposite direction of 1 (left in the figure). We make the point -3 which is at three times of length between 0 and 1, from 0 toward the opposite direction of 1 (left in the figure)... Similarly we determine the point of every negative integer -n.
Now, we will show the addition with the figure. For example, we take the point of 3, from the point toward the right, we take the point of the length between 0 and 5, then the point is of 3 + 5.
This figure shows the following relation.
Moreover, we will do the following computation. After clicking some of the buttons above, please click the "result" button. Also, after clicking any position on the line of the figure, please click any position under the line, and after that, please click the "Result" button.
This way is quite difficult, but it is useful a little to make it easy to understand the relation between multiplication and division.First, shown as above, we draw a line (horizontal line in the figure) and we make an integer correspond to the point on the line. Next, we draw another line (vertical line in the figure) and also we make an integer correspond to the point on the line.
To show multiplication with the figure, it is difficult,
but we do as follows.
For example, first, we take the point 3 on the horizontal line,
and next, we take the point 5 on the vertical line.
We draw the line which links the point taken on the horizontal line to
the point 1 of the vertical line.
We draw the line which is parallel to this line,
and passes through the point taken on the vertical line.
The point which this line and the horizontal line intersect
is the point of 3 * 5.
This figure shows the following relations.
Moreover, we will do the following computation. After clicking some of the buttons above, click the "Result" button. Also, after clicking any position on the horizontal line of the figure, click any position on the vertical line, and after that, click the "Result" button.