How to Multiply by Most Numbers
This blog post is a very quick run-down on how to multiply one number by another in your head.
There are, to be honest, a trillion (that's a million times a million!) different ways to multiply numbers. Some fast, some slow.
What I've compiled below is a quick guide to multiplying many of the commonest numbers you'll come across at GCSE and A-level — basically, your times tables.
Here goes!
Multiplying by 1
When multiplying a number by 1, your answer is simply the original number.
Example:
4 × 1 = 4
Multiplying by -1
When multiplying a number by -1, your answer is simply the negative of the original number.
Example:
4 × (-1) = -4
Multiplying by 10
When multiplying by 10, simply add a 0 after the original number.
Example:
12 × 10 = 120
Multiplying by 2
When multiplying a number by 2, you are simply doubling the original thing.
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If your original number is a whole number, you will generate an even number.
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If your original number ends in “.5” (point-five), then your answer will be an odd number.
Multiplying by 20
When multiplying by 20, simply multiply by 2 and then add a zero after the number.
Multiplying by 3
You can think of multiplying by 3 as being “twice-plus-another-one.”
Example:
3 × 12 = 2 × 12 + another 12 = 24 + 12 = 36
Multiplying by 30
When multiplying by 30, simply multiply by 3 and then add a zero after the number.
Multiplying by 4
Think of multiplying by 4 as “doubling, then doubling again.”
Example:
4 × 12 = 2 × 12 × 2 = 24 × 2 = 48
This is because 4 is double 2, and timesing by 2 is simply doubling. So when timesing by 4 you are simply doubling twice.
Multiplying by 5
You can think of multiplying by 5 as multiplying by 10 and then halving it — because 5 is half of 10.
Example:
12 × 5 = half of (12 × 10) = half of 120 = 60
Multiplying by 6
You can choose one of two routes:
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Triple, then double.
12 × 6 = double (12 × 3) = double 36 = 72
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Times by five, then add another one.
12 × 6 = 12 × 5 + another 12 = 60 + 12 = 72
Multiplying by 7
There aren't many easy shortcuts, but you can make your own.
Think of it as “5 of them plus 2 of them.”
Example:
7 × 12 = 5 × 12 + 2 × 12 = 60 + 24 = 84
Multiplying by 8
8 is double 4 — and we know the rule for 4 was to double something twice.
So for 8 × something, we simply double it three times over!
Example:
8 × 12 = double → double → double 12
double 12 = 24 → double again = 48 → double again = 96
(For this last step, think about doubling 50 = 100, then realising that 48 is 2 smaller than 50, so our final answer should be 4 (double-2) smaller than 100.)
Alternatively, you could think of multiplying by 10, then taking off two of the original number:
Example:
8 × 12 = 10 × 12 − 2 × 12 = 120 − 24 = 96
Multiplying by 9
The 9 times table has a nice pattern:
09, 18, 27, 36, 45, 54, 63, 72, 81, 90 —
the first digit increases, the second digit decreases.
After 10 × 9 = 90, it gets a bit messier (99, 108, etc.),
so here’s a reliable trick:
Multiply by 10 and then take away the original number.
Example:
12 × 9 = (12 × 10) − 12 = 120 − 12 = 108
This always works!
Multiplying by 11 and 12
When multiplying by 11, think “10 of the thing, plus another one.”
Example:
11 × 12 = 10 × 12 + another 12 = 120 + 12 = 132
You can think similarly for multiplying by 12 — “10 of the thing, plus another two.”
🎓 Final Thought
Notice how each rule builds from each of the others.
Multiplication isn’t just rote memorisation — it’s patterns and relationships between numbers.
Once you understand these, the whole times table becomes logical, beautiful, and intuitive — AND you get the added bonus of maths feeling far, far more simple than it did before, because (hopefully) recalling facts about numbers won't take quite so long.