What to notice
Every starting number has digits that add to 9 or a multiple of 9: 2 and 7 for 27, 4 and 5 for 45. That is the test for whether a number divides by 9 with nothing left over. 99 and 108 pass as well, since their digits add to 18 and to 9.
The finger trick runs backwards too: to find 36 ÷ 9, look for the finger with 3 fingers to its left and 6 to its right. That is the fourth finger, so the answer is 4.
Above 90, use the 10s instead: 99 ÷ 9 = 11 and 108 ÷ 9 = 12 are two facts worth learning on their own.
Nines also work as tens with a little taken off. 63 is a bit less than 70, and 70 ÷ 10 = 7, so 63 ÷ 9 is close to 7; check with 9 × 7 = 63. Estimating from the 10s is a useful habit for division in general, not only for this table.
How to practise at home
- Practise the tens-digit rule aloud: “72 ÷ 9: the tens digit is 7, one more is 8.”
- Play “in the 9s or not?” with the digit sum: 81 yes, 82 no, 63 yes.
- Pair each fact with the times table: “9 × 8 = 72, so 72 ÷ 9 = 8.”
- Use the drill on this page; once the tens-digit rule clicks, the 9s division facts often come quickly.
- Show the fact family for one fact a day: 9 × 6 = 54, 6 × 9 = 54, 54 ÷ 9 = 6 and 54 ÷ 6 = 9. Four facts for the price of one, and the divide-by-6 facts get a lift at the same time.
Slips to watch for
- Answering with the tens digit itself, such as 5 for 54 ÷ 9. Remind your child that it is one more.
- Using the tens-digit rule for 99 or 108, where it breaks. Those two are 11 and 12.
- Answering 9 for 72 ÷ 9 because 72 is also 8 × 9. In the fact family, 72 ÷ 9 = 8 and 72 ÷ 8 = 9.