How to learn the times tables

A times table is a list of a number's multiples: the 3 times table is 3, 6, 9, 12 and on up to 30. Knowing the tables by heart makes long multiplication, long division and fractions much quicker, because they are built out of these facts.

How to learn them

1. Start with the 2, 5 and 10 times tables. They have patterns you can see, and most schools begin with them.
2. Then learn the tables that come from those. The 4 is the 2 doubled, and the 8 is the 4 doubled. The 6 is the 3 doubled.
3. Turn every new fact round. Once you know 3 × 7, you know 7 × 3, so each fact you learn counts twice.
4. Practise the facts out of order. Chanting 1 × 7, 2 × 7, 3 × 7 means counting up the list every time you need one fact.
5. Pick out the few facts that will not stick and work on a handful at a time. Say each one as a whole, "seven eights are fifty-six", a little every day.

Worked examples

A trick for every table

×2: double the number. 2 × 7 = 7 + 7 = 14. Every answer is even.

×3: count in 3s. The digits of every answer add up to 3, 6 or 9, which is the rule for 3: 3 × 8 = 24, and 2 + 4 = 6.

×4: double, then double again. 4 × 6 is 6 doubled, 12, doubled again, 24.

×5: every answer ends in 0 or 5. It is half of 10 times: 5 × 8 is half of 80, which is 40.

×6: double the 3 times table. 3 × 7 = 21, so 6 × 7 = 42. When 6 multiplies an even number, the answer ends in that number: 6 × 4 = 24, 6 × 6 = 36, 6 × 8 = 48.

×7: the one children dread, but the other tables already hold nearly all of it. Learn it last and turn the facts round, and only 7 × 7 = 49 is new.

×8: double three times. 8 × 6 is 6 doubled, 12, then 24, then 48.

×9: ten times, take away once. 9 × 6 = 60 − 6 = 54. Or hold up ten fingers and fold down the sixth: the 5 fingers to its left are the tens and the 4 to its right are the ones, 54.

×10: every digit moves one place to the left, and a 0 fills the ones. 10 × 7 = 70.

What about 11 and 12?

The app stops at 10, like many schools around the world. In England children are expected to know up to 12 × 12 by the end of Year 4, when they take the multiplication tables check.

11 is easy up to 9: write the digit twice, so 11 × 7 = 77. 12 is the 10 and the 2 tables added together: 12 × 7 = 70 + 14 = 84.

Why there are fewer facts than it seems

The tables from 2 to 10 hold 90 facts. Many need no learning: anything times 1 is itself, and the 10 table is the easiest of all. Turning facts round halves the rest. From 2 × 2 to 9 × 9 there are only 36 different facts, and once the 2, 5 and 10 tables are known, 21 are left.

Facts turn round because of the dots. 3 rows of 4 are also 4 columns of 3, the same 12 dots looked at from the side. So 3 × 4 and 4 × 3 are one fact, not two.

Splitting a hard fact works for the same reason. 7 eights can be put in two piles, 5 eights and 2 eights. Nothing is added or lost, so 40 + 16 is still 7 × 8. Long multiplication is this same idea with bigger numbers.

Where mistakes happen

• Reading × as +. 3 × 4 is three 4s, which makes 12. Putting 3 and 4 together gives 7.
• Mixing up 7 × 0 and 7 × 1. One group of 7 is 7, so 7 × 1 = 7. No groups of 7 is nothing, so 7 × 0 = 0.
• Swapping neighbours. 7 × 8 = 56 and 6 × 9 = 54 are close, and so are 6 × 8 = 48 and 7 × 7 = 49. A trick catches it: 5 + 4 = 9, so 54 belongs to the 9 table, and 56 does not.
• Thinking "add a 0" always works for 10. It works for whole numbers, but 10 × 0.5 is 5, not 0.50. What really happens is that every digit moves one place to the left.

Questions people ask

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