In this way we repeat the multiplicand as many times as there are figures in the multiplier; but instead of writing beside these figures the words units, tens, etc., we indicate this with zeros, which, for the sake of clearness, we fill in till they resemble large dots.
The child already knows, from his previous exercises, that zero indicates the position of a figure and that multiplying by ten changes this position. Therefore zeros in the multiplier would cause a corresponding change of position in the figures of the multiplicand.
The accompanying figure shows clearly what it is not so easy to explain in words.
Fig. 3.
We are now ready for the usual procedure of multiplication. A child of seven years reaches this stage very easily after having done our preliminary exercises, and then it does not matter to him how many figures he has to use. Indeed, he is very fond of working with numbers of unheard of figures, as is shown in the following example—one of the usual exercises done by the children, who of themselves choose the multiplicand and the multiplier; the teacher would never think of giving such enormous numbers. They can now perform the operation
22,364,253 × 345,234,611
22364253 ×
345234611
22364253
22364253
134185518
89457012
67092759
44728506
111821265
89457012
67092759
7720914184760583
without analysis of factors and without help from the frames but by the method commonly used. This may be seen by the way in which the example is written out and then done by the child.