Times table tricks that you can explain.
A good multiplication trick does more than produce an answer. It gives you a route back to a fact you already know. These patterns work for whole numbers of any size, not just the first ten entries of a table.
The 9 multiplication table trick: multiply by 10, then subtract once
Nine is one less than ten. For 9 × 7, calculate 10 × 7 = 70, then take away one more 7. The answer is 63. The same reasoning works beyond the table: 9 × 14 = 140 − 14 = 126.
9 × 7 = (10 × 7) − 7 = 63
This is a reliable check as well as a trick. If you get a result larger than ten groups of the number, you know something went wrong.
The 6 times table: start with five groups
Multiplying by 5 is often easy because it is half of multiplying by 10. Add one more group to reach 6. For 6 × 8, half of 10 × 8 is 40; add 8 to get 48.
6 × 8 = (5 × 8) + 8 = 48
The 7 times table: five groups plus two
Split seven into five and two. Then 7 × 8 is 5 × 8 + 2 × 8, or 40 + 16 = 56. This takes two small products rather than recalling 7 × 8 from memory. As that fact becomes familiar, you can keep the shortcut as a way to check it.
7 × 8 = 40 + 16 = 56
The 8 times table: ten groups minus two
Eight is two less than ten. For 8 × 7, begin with 10 × 7 = 70 and remove 2 × 7 = 14. That leaves 56. You can also double three times: 7 → 14 → 28 → 56. Choose the path you find easier to hold in your head.
8 × 7 = 70 − 14 = 56
The 11 times table trick
Up to 11 × 9, the answer is the digit written twice: 11 × 7 = 77. After that, use the neighbour rule: keep the outside digits and add them in the middle. For 11 × 12, keep 1 and 2 and put 1 + 2 = 3 between them: 132.
11 × 12 = 1 (1 + 2) 2 = 132
The same rule works for much bigger numbers. See the full multiply by 11 trick.
The 12 times table trick: ten groups plus two
Split 12 into 10 and 2. For 12 × 7, ten sevens are 70 and two sevens are 14, so the answer is 84. The hardest fact in the table becomes easy the same way: 12 × 12 = 120 + 24 = 144.
12 × 7 = 70 + 14 = 84
The best way to learn times tables
- Understand before memorising. Draw 3 rows of 4 dots to see why 3 × 4 = 12.
- Learn the easy tables first. ×2, ×10 and ×5, then use them to reach the rest.
- Use turnaround facts. 3 × 8 = 8 × 3, which nearly halves the facts to learn.
- Work out the hard ones. Use the tricks on this page instead of guessing.
- Practise a little every day. Five minutes of mixed facts beats a long session once a week.
For fun ways to learn times tables, try our multiplication games for kids. Teaching a child? Read how to teach multiplication for the full order.
How to make multiplication facts stick
Pick two facts you hesitate over. Derive each answer slowly, say the relationship aloud, then check the result by reversing the factors or using a second split. For example, 7 × 8 and 8 × 7 are the same 56, even though the two routes above look different. Revisit those facts in a later short session instead of drilling the entire table at once.
Where the Trachtenberg method fits
These are general place-value tricks, not Trachtenberg rules. The Trachtenberg method gives a more specific digit-by-digit procedure for a multiplier. If you like predictable steps, compare the ideas with our ×11 and ×12 multiplication guide. If you want a larger-number example first, see how to multiply in your head.