| 73 | |
| 25 |
| 1460 | = | 20 | times. |
| 365 | = | 5 | „ |
| 1825 | = | 25 | „ |
and to work the same sum in a variety of ways, e.g., multiply by 5 × 5; by 100, and divide by 4; by 30, and take off 5; by 10, halve and by 10 again and halve:—
| 73 | |
| 5 |
| 365 | = | 5 | times. |
| 5 | |
| 1825 | = | 5 | × | 5 | times. |
| 4 | 7300 | = | 100 times. |
| | 1825 | = | 1⁄4 of 100, or 25 times. |
| 73 | |
| 30 |
| 2190 | = | 30 | times. |
| 365 | = | 5 | „ |
| 1825 | = | 25 | „ |
| 2 | 730 | = | 10 | times. | |
| | 365 | = | 5 | „ |
| 3650 | = | 50 | „ |
| 1825 | = | 1⁄2 50 = 25 times. |
It is well to accustom children to begin to multiply with the left-hand figure, as we shall see later. Thus we get the most important part first.
Division.It should be insisted on that division is undoing multiplication—that if we divide 63 by 9, we are finding a number 7 which when multiplied by 9 gives 63. In working division sums it is better to put the quotient over the dividend, and the children should be ready to explain each step thus: Divide 3496 nuts amongst four schools equally. None will get as many as 1 thousand. They will get, out of 34 hundreds, 8 hundreds each; of 29 tens, 7 tens each; of 16 units, 4 each.
Long division should be fully explained thus: Divide 43921 amongst 23 people. We see that no one will have as much as 1 ten-thousand. Out of 43 thousands, each can have 1 thousand, and there will be 20 thousands left, that is, 200 hundreds; adding 9 we get 209 hundreds. We give 9 to each and 2 hundreds or 20 tens are left. 22 tens do not give one each; they equal 220 units. Of the 221 units we give 9 to each. Some dispense with the written multiplication. This seems to me to strain too much young children’s attention, and to lead to loss of time.