Explanation
For every multiplication of 9 from 1 x 9 up to 9 x 9, the two digits of the answer always add up to 9. That makes it easy to check an answer, or even to recall it if you've forgotten it.
All nine facts, one through nine:
- 1 x 9 = 09 (0 + 9 = 9)
- 2 x 9 = 18 (1 + 8 = 9)
- 3 x 9 = 27 (2 + 7 = 9)
- 4 x 9 = 36 (3 + 6 = 9)
- 5 x 9 = 45 (4 + 5 = 9)
- 6 x 9 = 54 (5 + 4 = 9)
- 7 x 9 = 63 (6 + 3 = 9)
- 8 x 9 = 72 (7 + 2 = 9)
- 9 x 9 = 81 (8 + 1 = 9)
Why this works: multiplying by 9 is the same as multiplying by 10 and then subtracting the number once (9 x n = 10 x n − n). That subtraction always lowers the tens digit by 1 and raises the ones digit by 9 (borrowing 10 in the process), so the two digits keep adding up to 9 no matter which number you started with.
Bonus finger trick: hold up both hands, 10 fingers total. To multiply 9 by a number from 1 to 9, fold down that numbered finger (counting from the left). The fingers to the left of the folded one give the tens digit, and the fingers to the right give the ones digit. For example, to find 9 x 4, fold down the 4th finger: 3 fingers remain on the left (tens digit 3) and 6 fingers remain on the right (ones digit 6), giving 36. See Multiplication of 9 times any number from 1 to 10 for a picture of this trick.