Times Nine Pattern

Look at the 9th row ... with the red border. Do you see any pattern whatsoever?

The first digit is one less than the number by which you multiply nine.
For example: When you multiply 9 x 8, the first digit of the answer is 7.
Mouseover the different cells in the 9th row to see the two-step operation
  1 2 3 4 5 6 7 8 9 10
1 1 x 1 = 1 1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 5 1 x 6 = 6 1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 1 x 10 = 10
2 2 x 1 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20
3 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30
4 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40
5 5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50
6 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60
7 7 x 1 = 7 7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42 7 x 7 = 49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 70
8 8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80
9 9 x 1 = 9 9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45 9 x 6 = 54 9 x 7 = 63 9 x 8 = 72 9 x 9 = 81 9 x 10 = 90
10 10 x 1 = 10 10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50 10 x 6 = 60 10 x 7 = 70 10 x 8 = 80 10 x 9 = 90 10 x 10 = 100

Logical explanation for this pattern: Ten 8s is 80, so the first digit is 8. But we do not have ten 8s, we have nine of them only. So when we subtract the extra 8, we get seventy something, so the first digit is 7.

The pattern works for any whole number from 1 to 9 multiply by nine. If number is more than 9, you have more than two digits in the answer, so the whole pattern is different.

Times Nine Pattern: To multiply a number by nine, multiply that number by ten (which is easy!) and then subtract the number.

Another example: 9 x 2

  1. 10 x 2 = 20
  2. 20 minus 2 = 18

Times Nine "Trick"

Hold both your hands in front of you. Count as many fingers as the number by which you multiply nine, starting from the left. Bend that finger. The number of fingers to the left of the bent finger will be the first digit of the answer, and the number of fingers to the right of it will be the second digit of the answer.


Example: 9 x 7

Count the seventh finger from the left and bend it. There are six fingers to the left of the bent finger, and three fingers to the right. So we have 9 x 7 = 63.

Now you try ... multiplying 9 x 3. Does it work?


Times Ten for Free Times 9 Times Five Pattern
Reproduced with permission from Maria Droujkova, Natural Math
Redesigned by "Parenting the Next Generation"