Mental math tricks: seven shortcuts people actually use
Fast mental arithmetic isn't about calculating faster, it's about picking a shorter route. Seven shortcuts with the reason each one works, and how to practise them in two minutes a day.
There's a common misconception about mental arithmetic: that people who do it fast simply think fast. That isn't it. People who calculate quickly in their heads almost never solve the sum they were given — they swap it for an easier one that gives the same answer.
That can be learnt. It's half a dozen shortcuts, and each one has a reason behind it worth understanding, because a trick you memorise without understanding is gone in a week.
1. Left to right, the opposite of school
On paper we add starting from the units, because that's how carrying works. In your head it's the other way round: start with what weighs most.
486 + 257 → 400 + 200 = 600 → 80 + 50 = 130 → 6 + 7 = 13 → 743.
Why it works: your working memory holds very few things at once. Going left to right, at every step you have a single number in your head that keeps growing. Going right to left, you have to hold loose digits until the end.
2. Round, then correct
Hardly any ugly sum is really ugly. It's one step away from an easy one.
47 + 38 → 47 + 40 = 87 → 87 − 2 = 85.
312 − 98 → 312 − 100 = 212 → 212 + 2 = 214.
The rule: round to the nearest ten or hundred, do the sum, then give back what you borrowed. The classic mistake is giving it back the wrong way, so say it out loud as you round: "I added two too many, I need to take two off."
3. Times 5, times 25, times 9
These three come up constantly and all three have a shortcut.
- Times 5 is times 10, halved.
34 × 5→340 / 2= 170. - Times 25 is times 100, divided by four.
18 × 25→1800 / 4= 450. - Times 9 is times 10 minus the number.
7 × 9→70 − 7= 63. It works with big numbers too:43 × 9→430 − 43= 387.
Why: 5 is 10/2, 25 is 100/4 and 9 is 10−1. Multiplying by 10 or 100 is free, so it pays to turn any factor into "something round, adjusted".
4. Double and halve
If one factor is even, you can halve it while doubling the other. The answer doesn't change.
16 × 25 → 8 × 50 → 4 × 100 = 400.
This is the most profitable shortcut of all, because it turns awkward multiplications into multiplications by round numbers. It works because you're dividing and multiplying by two at the same time, and the two cancel out.
5. Squares of numbers ending in 5
35²: take the 3, multiply it by the next number up (4) → 12. Stick 25 on the end → 1225.
85² → 8 × 9 = 72 → 7225.
It isn't magic: (10a+5)² = 100·a·(a+1) + 25. Work through it once with the formula in front of you and you'll never forget it.
6. Subtract by counting up
Subtraction is the operation that copes worst with being done mentally, because chained borrows get lost. The fix is not to subtract at all: measure the distance.
73 − 46: from 46 to 50 is 4, from 50 to 73 is 23. Total 27.
It's exactly what a shopkeeper does when handing back change, which is why they almost never get it wrong.
7. Percentages can be flipped
x % of y is always the same as y % of x. It sounds like a curiosity and it's a brutal shortcut.
18 % of 50 looks awkward. 50 % of 18 is 9. It's the same number.
For everything else, work out 1 % by moving the decimal point two places and multiply: 7 % of 240 → 1 % is 2.4 → × 7 = 16.8.
How to actually practise this
The classic mistake is sitting down for half an hour of sums. It doesn't work, because mental arithmetic decays through lack of automation, not lack of effort.
What works are short, frequent bursts: two or three minutes, every day, with sums that force you to pick a shortcut. The important part isn't getting them right, it's noticing the moment you choose the route. At first you'll choose after starting; within weeks, you'll choose before.
In MenteBrillante that training is the Quick Maths puzzle, with timed rounds that get harder. And if what interests you is the other side of numbers — the patterns — there are also number sequences, which are what show up in aptitude tests.
You can try them in the web version, with nothing to install.
What these tricks won't give you
An honest warning to finish: calculating quickly in your head does not make you better at maths. They're different things. These shortcuts are fluency, not reasoning, in the same way that reading fast isn't the same as understanding what you read.
What they do is remove friction. When you don't have to stop and calculate, your head stays free for what you were actually doing: comparing two offers, splitting a bill, working out whether a discount is worth it. That's where you notice it.