The 9s look like a hard table, and children often meet them among the later tables. The good news is that they hide more shortcuts than almost any other table. This guide shows three of them, explains why each one works, and ends with a two-minute daily plan.
Hold up all 10 fingers and fold down the finger for the number you are multiplying by 9. The fingers to the left of the fold are the tens, and the fingers to the right are the ones. For 3 × 9, fold finger 3 and read 2 and 7, which is 27.
This post covers three tricks:
Hold both hands out in front of you with your palms facing down. Number your fingers from 1 to 10, going from left to right and counting the thumbs. Your left little finger is finger 1, your two thumbs are fingers 5 and 6, and your right little finger is finger 10.
Now fold down one finger:
3 × 9: fold finger 3, the middle finger of your left hand. There are 2 fingers on the left and 7 on the right, so the answer is 27.
7 × 9: fold finger 7, the pointing finger of your right hand. There are 6 fingers on the left and 3 on the right, so the answer is 63.
The first and last facts look odd, but they follow the same rule. For 9 × 1, fold finger 1: there are no fingers on the left and 9 on the right, so that is 0 tens and 9 ones, which is 9. For 9 × 10, fold finger 10: there are 9 fingers on the left and none on the right, so that is 9 tens and 0 ones, which is 90.
Parent tip: ask your child to say the whole sum aloud ("seven nines are sixty-three"), then check it on paper. Saying it helps the fact stick, so the fingers are needed less often. If a picture helps, Sketchplanations has a drawing of the 3 × 9 example.
This part is optional, and it suits older children who like to know the reason.
When you fold finger n, there are n - 1 fingers on the left and 10 - n fingers on the right. Those always add up to 9, because one finger out of 10 is folded. Reading them as tens and ones gives:
10(n - 1) + (10 - n) = 10n - 10 + 10 - n = 9n
That is exactly 9 lots of the number. Check it with finger 4: there are 3 tens and 6 ones, so 30 + 6 = 36, and 4 × 9 = 36.
Write out the table and look at the digits. If your child already skip counts by 9s, this is the same list. We have written 9 as 09 so that the pattern is easy to see.
| Fact | Answer | Add the digits |
|---|---|---|
| 9 × 1 | 09 | 0 + 9 = 9 |
| 9 × 2 | 18 | 1 + 8 = 9 |
| 9 × 3 | 27 | 2 + 7 = 9 |
| 9 × 4 | 36 | 3 + 6 = 9 |
| 9 × 5 | 45 | 4 + 5 = 9 |
| 9 × 6 | 54 | 5 + 4 = 9 |
| 9 × 7 | 63 | 6 + 3 = 9 |
| 9 × 8 | 72 | 7 + 2 = 9 |
| 9 × 9 | 81 | 8 + 1 = 9 |
| 9 × 10 | 90 | 9 + 0 = 9 |
Read down the Answer column. The tens digit climbs from 0 to 9 while the ones digit falls from 9 to 0.
Suppose your child says that 9 × 6 is 53. Add the digits: 5 + 3 = 8. That isn't 9, so something has gone wrong. The check can miss a mistake, though, because 45 also adds to 9 and it isn't the answer to 9 × 6. A pass tells you the answer could be right, not that it is.
Take 9 × 7. The tens digit is one less than the number you are multiplying by, so it starts with 6. The ones digit is whatever brings the total up to 9, and 9 − 6 = 3. Put them together to get 63.
The tidy version only holds for the first ten facts. 9 × 11 = 99, and 9 + 9 = 18, not 9. 9 × 12 = 108 does add to 9, since 1 + 0 + 8 = 9, but it has three digits, so the up-and-down pattern has ended.
There is a bigger rule underneath: the digits of any multiple of 9 add to a multiple of 9. If you keep adding, you always end on 9, so 99 gives 18 and then 1 + 8 = 9. Our post on digital roots explains that idea in full.
9 is one less than 10, so 9 lots of a number is 10 lots of it, take away one lot. In short, 9 × n = 10 × n - n.
This is the trick that keeps going after the fingers run out:
It also helps with the facts where folding feels slow, once your child is happy multiplying by 10. And it leads somewhere: working from a nearby 10, 100 or 1000 is the idea behind the Vedic Nikhilam method for numbers close to those bases.
| Trick | Best for | Works up to |
|---|---|---|
| Fingers | Seeing the answer, especially for beginners | 9 × 10 |
| Digit pattern | Checking an answer | 9 × 10 as it stands; beyond that, keep adding the digits |
| Ten minus one | Working out a fact in your head | Any size |
These tricks help children reach the right answer while their memory catches up. The goal is still to know the facts without them, so that 7 × 9 comes to mind straight away. For a plan that covers every table, not only the 9s, see how to learn times tables fast.
Go to the times tables page, find row 9 of the chart and press its "Practise" button to get 10 quick questions, which appear above the chart. On a phone, scroll the chart sideways to reach the button, because it sits after the 12 number columns. Finish with a round of the multiplication game if your child wants more. Two minutes a day is enough. The questions can go up to 9 × 12, so use ten minus one for 9 × 11 and 9 × 12 on any day:
For most children it is the finger method. Fold down the finger for the number you are multiplying by 9, then read the fingers on the left as tens and the fingers on the right as ones. For 7 × 9, that gives 6 and 3, which is 63.
Folding finger 4 leaves 3 fingers on the left and 6 on the right, so you read 36, and 4 × 9 = 36. The left side is always one less than the number you chose, and the right side makes up the rest of the 9 standing fingers. That always comes to 9 lots of the number.
Adding 9 is the same as adding 10 and taking away 1. So each step moves the tens digit up by 1 and the ones digit down by 1, and their total stays the same. It starts at 0 + 9 = 9, so it stays at 9 all the way to 90.
Not in the simple form. 9 × 11 = 99, and its digits add to 18, although adding again gives 1 + 8 = 9. 9 × 12 = 108 does add to 9, but the tens-up, ones-down pattern has already stopped.
Multiply by 10, then take away the number once. For example, 9 × 25 = 250 − 25 = 225. This works for a number of any size, and it only uses skills your child already has.
On the times tables page, press the "Practise" button in row 9 of the chart for 10 quick questions (on a phone, scroll the chart sideways to reach it), then play the multiplication game. A couple of minutes each day works better than one long session at the weekend.
Yes. The tricks give your child a way to find an answer and a way to check it, but remembering the fact is faster and leaves more attention for bigger problems. As the facts become familiar, encourage them to answer first and use a trick only to check.