1/4 + 1/7 + 1/9 + 1/10.
In order to find the sum of the fraction reduced to decimals, it is necessary to read only the number at the outer edge of the last sector.
Using this as a basis, it is very easy to develop an arithmetical idea. Instead of 1, which represents the whole circle, let us write 100, which represents its subdivisions when used for decimals, and let us divide the 100 into as many parts of a circle as there are sectors in the circle, and the reduction is made. All the parts which result are so many hundredths. Hence:
1/4 = 100 ÷ 4 = 25 hundredths: that is, 25/100 or 0.25.
The division is performed by dividing the numerator by the demoninator:
1 ÷ 4 = 0.25.
Third Series of Insets: Equivalent Figures. Two concepts were given by the squares divided into rectangles and triangles: that of fractions and that of equivalent figures.
There is a special material for the concept of fractions which, besides developing the intuitive notion of fractions, has permitted the solution of examples in fractions and of reducing fractions to decimals; and it has furthermore brought cognizance of other things, such as the measuring of angles in terms of degrees.
For the concept of equivalent figures there is still another material. This will lead to finding the area of different geometric forms and also to an intuition of some theorems which heretofore have been foreign to elementary schools, being considered beyond the understanding of a child.