5 min read
Everyone has a calculator in their pocket, so mental math speed looks like a solved problem — until you’re splitting a bill, checking whether a “40% off” sticker actually beats the smaller size, or trying to follow a conversation full of numbers without stopping to type them into a phone. Fast mental arithmetic is not about being a human calculator; it’s a small set of reusable tricks that turn ugly numbers into easy ones. Here are the ones that actually pay off.
The single highest-value trick in mental math is refusing to do arithmetic on an awkward number when a nearby round one is available. To add 398, add 400 and subtract 2. To subtract 19, subtract 20 and add 1 back. This works because addition and subtraction are forgiving of this kind of detour — the “adjust” step is almost always simpler than the original problem — and it turns numbers ending in 7, 8, 9 or 1, 2 from obstacles into the easiest numbers in the whole calculation.
Multi-digit addition and subtraction get much easier once you stop trying to process a whole number as one block and instead work with its parts. 47 + 35 is friendlier as (40 + 30) + (7 + 5), giving 70 + 12, giving 82 — two easy steps instead of one hard one. The same move works for multiplication: 6 × 23 is 6 × 20 plus 6 × 3, which is 120 + 18, which is 138. Nothing here is a new fact to memorise; it’s just choosing an order of operations that keeps every intermediate number small and manageable instead of large and error-prone.
Doubling and halving are two of the fastest operations the brain does, so it’s often worth trading a harder multiplication for an easier doubling-and-halving pair. Multiplying by 5 is the same as multiplying by 10 and halving the result — 5 × 48 becomes 480 ÷ 2, which is 240. Multiplying by 4 is doubling twice. Multiplying by 25 is dividing by 4, then multiplying by 100. None of these are separate facts to learn; they all lean on the same underlying trick of swapping an unfamiliar operation for two familiar, faster ones.
A handful of specific patterns save real time once they’re automatic. Multiplying by 9 is often faster as multiplying by 10 and subtracting the original number once — 9 × 23 is 230 − 23, which is 207. Multiplying by 11 for a two-digit number is the two digits added together and dropped in the middle, when there’s no carrying involved — 11 × 34 is 3, then 3 + 4 = 7, then 4, giving 374. Squaring a number that ends in 5 has a clean shortcut: multiply the leading digit by the next number up, then put 25 on the end — 45² needs 4 × 5 = 20, then 25 on the end, giving 2025, no long multiplication required. It works because a number ending in 5 is always ten times some digit plus five, and squaring that expression algebraically lands on exactly “leading digit times the next one up, then 25” — the shortcut isn’t a coincidence, it’s that algebra pre-computed.
Every trick above still has to be executed somewhere, and that somewhere is working memory — the same small mental scratchpad that holds a phone number for a few seconds before you dial it. Mental arithmetic fails less often because someone doesn’t know a shortcut and more often because they run out of scratchpad space holding intermediate results while computing the next step, which is exactly why breaking a big number into small chunks helps: each chunk is a lighter load to carry. If that idea interests you, our guide on training working memory goes into why that scratchpad is so small and what genuinely helps it hold more.
Like any other fast, accurate skill, mental math speed responds to focused practice far more than to passive exposure — reading about tricks does very little compared to actually using them under a bit of time pressure. Short, frequent sessions beat rare long ones, because the goal is making each trick automatic rather than something you have to consciously recall mid-calculation. Practising against a clock specifically also trains the second half of the skill that raw accuracy practice skips: deciding fast which trick applies to the number in front of you, not just executing it correctly once you’ve picked one.
A dedicated arithmetic sprint is on its way to the arcade, but in the meantime the games already here train the two skills mental math actually depends on. Memory Path is a clean stand-in for the working-memory load of holding intermediate results while you calculate the next step — the longer the path, the more you’re carrying at once, exactly like a multi-step sum. Timing Tap trains the “decide fast, commit, don’t second-guess” instinct that separates someone who knows the tricks from someone who can actually use them under a clock, which our reaction time guide looks at in more depth.