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← BlogOct 3, 20263 min read

The 9 times table: ten of them, minus one

Heron

I'm Heron. I help people do math in their heads, and I counted the 9s on my fingers for years.

It turns out the fingers were doing real arithmetic. Let's find out what they counted.

The 9 times table from 1 to 12

Here is the whole chart: twelve facts from the multiplication table for 9. The next section turns each into an easy ten and a small subtraction.

The table climbs in jumps of nine, from 9 up to 108.

Now read the first ten answers two digits at a time. The tens climb 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, while the units fall back from 9 to 0.

So those two digits always add to 9. A wrong answer gives itself away.

One answer steps out: 9 × 11 = 99. Its digits make 18, so add them once more and the 9 is back.

Why ten of them, minus one, works

Nine is 10 minus 1. That is the whole trick: take ten of the number, then give one back.

Step 1 of 5the fact we want

9 × 7

Tap through and the pieces are 70, 7, and 63: one easy ten, one subtraction, done.

The finger trick runs this same sum. Hold up ten fingers, fold down the seventh, and six stand to its left with three to its right, which reads 63.

The fold is the subtraction. Left of it are the tens, right of it the units, and nine fingers always stand.

The hands stop at 9 × 10. There is no eleventh finger, so the last two stay with the ten: 110 take away 11 is 99, and 120 take away 12 is 108.

Twelve facts, and five to learn

Three of the twelve come free. 9 × 1 is 9, 9 × 10 is 90, and 9 × 11 is a nine written twice.

Eight of the first ten answers come in mirror pairs. Learn one half, and the other half is that answer read backwards.

Each line is one answer and the same digits turned around. 9 × 2 is 18, and 81 is that read the other way: 9 × 9.

Why the mirrors happen: the tens digit climbs while the units digit falls, so a reversed pair meets the chart from the other end.

That leaves five answers to learn: one half from each pair, and 9 × 12 = 108.

One honest warning: a mirror saves learning, not time. England's check gives six seconds a question, so spotting 81 as the flip of 18 still has to get quick.

Practice the 9 times table

Ten questions, friendly ones first. Get one wrong and the box hands you the ten to start from.

9 × 2 =

Same rules as above. You've got this.

9 × 5 =

Same rules as above. You've got this.

9 × 3 =

Same rules as above. You've got this.

9 × 11 =

Same rules as above. You've got this.

The next six are where the subtraction earns its keep. Say both pieces out loud.

9 × 6 =

Same rules as above. You've got this.

9 × 4 =

Same rules as above. You've got this.

9 × 9 =

Same rules as above. You've got this.

9 × 12 =

Same rules as above. You've got this.

9 × 7 =

Same rules as above. You've got this.

9 × 8 =

Same rules as above. You've got this.

The 9s in England's tables check

England counts the 9s among its hardest. Year 4 there takes a multiplication tables check, 25 questions at six seconds each, and the tables it names as most difficult are the 6, 7, 8, 9, and 12 times tables.

The questions come from the 121 facts in the 2 to 12 tables, and every version asks between two and four from the 9s.

No version leaves them out. The 2s and the 10s can be dropped completely, the 9s cannot.

Year 4 gets there: in 2025 the most common result was full marks, and 37% of eligible pupils scored 25 out of 25.

Rounding up to a ten and paying the difference back is the habit behind grown-up mental arithmetic, with a question a day in our mental math practice. The 3 times table, the 4 times table, the 7 times table, the 8 times table, and the 12 times table sit next door.

What to remember

Heron
  • Ten of them, minus one. 10 × 8 is 80, give one 8 back, and 9 × 8 is 72.
  • The digits of the first ten answers add to 9. If they come to anything else, the answer is wrong.
  • Five answers to learn, seven that come free. Four of the free ones are mirrors.

Which one of the 9s gives you the most trouble?

FAQ

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