TablesMultiplication table tricks that really work
A trick is worth learning only if it is true every time and you understand why. The ones below are all plain arithmetic in disguise. Each comes with the reason it works, so that it can be trusted and so that it is not forgotten.
The finger trick for the table of 9
Hold both hands up, palms away from you, and number the fingers 1 to 10 from the left. To find 9 × 4, fold down finger number 4. Count the fingers to the left of the fold: 3. Count the fingers to the right: 6. The answer is 36. For 9 × 7, fold finger 7: 6 on the left, 3 on the right, 63.
Why it works: 9 times a number is 10 times the number minus the number. Taking one away from the tens and making the units up to 9 is exactly what folding one finger does.
Finger multiplication for 6, 7, 8 and 9
This old method gives any product from 6 × 6 to 10 × 10. On each hand, a closed fist stands for 5. Raise one finger for 6, two for 7, three for 8, four for 9. To find 7 × 8, raise two fingers on one hand and three on the other.
- Count all raised fingers: 2 + 3 = 5. These are tens, so 50.
- Multiply the folded fingers on one hand by those on the other: 3 × 2 = 6.
- Add: 50 + 6 = 56.
Why it works: if the numbers are 5 + a and 5 + b, the method gives 10(a + b) + (5 − a)(5 − b), which multiplies out to 25 + 5a + 5b + ab, the same as (5 + a)(5 + b).
Doubling chains: 2, 4, 8, 16
To multiply by 4, double twice. By 8, double three times. By 16, four times. For 8 × 13: 26, 52, 104. Halving runs the chain backwards, which is handy for division by 4 and 8.
Multiplying by 5
Multiply by 10 and halve. 5 × 46 is half of 460, which is 230. It works because 5 is half of 10.
Multiplying by 11
For a two-digit number, write the two digits and put their total between them: 11 × 35 gives 3, 8, 5, so 385. When the total is more than 9, carry one to the left digit: 11 × 67 gives 6, 13, 7, which becomes 737. It works because 11 × 35 is 350 + 35, and adding those two lines the digits meet in the middle.
Near a round number: 9, 19, 29, 99
Multiply by the round number and take one lot away. 19 × 7 is 140 − 7 = 133. 99 × 6 is 600 − 6 = 594. The same idea handles 18 (twenty times minus two lots) and 98.
Multiplying by 25
Multiply by 100 and divide by 4, since 25 is a quarter of 100. 25 × 36 = 3600 ÷ 4 = 900.
Squaring a number that ends in 5
Take the tens digit, multiply it by the next number up, and write 25 after it. For 35 × 35: 3 × 4 = 12, so the answer is 1225. For 75 × 75: 7 × 8 = 56, so 5625. There is more on this on the squares and cubes page.
Splitting any table
Every table above 10 can be split into "ten times" plus a small table. 17 × 6 is 60 + 42. 23 × 8 is 160 + 24. This is the distributive law, and it is the same step used later in long multiplication and in algebra. If a child learns only one method from this page, it should be this one.
Tricks to be careful with
"Add a zero to multiply by 10" breaks with decimals. Rhymes and stories for single facts help some children but give no way to check the answer. Prefer tricks that explain themselves, like the ones above.