The Table of 9's
There is a peculiar combination of figures in this table of 9's, which, if once noticed and perceived, will make this one of the easiest of the tables.
| 9 × 2 = 18 (1 + 8 = 9) | 9 × 8 = 72 (7 + 2 = 9) |
| 9 × 3 = 27 (2 + 7 = 9) | 9 × 9 = 81 (8 + 1 = 9) |
| 9 × 4 = 36 (3 + 6 = 9) | 9 × 10 = 90 (9 + 0 = 9) |
| 9 × 5 = 45 (4 + 5 = 9) | 9 × 11 = 99 (2 9's) |
| 9 × 6 = 54 (5 + 4 = 9) | 9 × 12 = 108 (1 + 0 + 8 = 9) |
| 9 × 7 = 63 (6 + 3 = 9) |
Notice that the two digits of each answer always add up to make 9, and that each first digit of the answer is just one less than the multiple. For example, 9×5=45, the answer will begin with one less than the multiple 5, and the two digits of the answer must add to make 9, therefore it can be nothing but 4 and 5, or 45. This is true in all cases except 9×11 an already known answer, but also only 9's in this answer. This simple idea, when once understood, will master the table of 9's.
Be sure that the children realize that 7×4 in the tables of 7's are the same in value as 4×7, so that the answer to 7×4 becomes familiar with learning the table of 4's. Ask the question both ways 7×4 and 4×7.