Every multiplication fact, every times table and every square root — each with the answer, the shortcut and a drill
Mental arithmetic is one skill made of a few hundred small facts. Once each fact is instant, everything built on top of it — long multiplication, dividing, fractions, percentages, unit conversion — stops being slow. This section has a page for every one of those facts, and a timed drill to turn recognition into recall.
There is a page for every multiplication fact from 2 × 2 to 20 × 20: 190 of them. Each one shows the answer, where it comes from, the quickest shortcut for that particular pair, the two division facts that travel with it, and the facts either side that get answered by mistake.
Because 7 × 8 and 8 × 7 have the same answer, they share one page rather than competing for the same search — the reversed address redirects to it.
The ones that cause the most trouble are the middle of the grid: 7 × 8 = 56, 6 × 8 = 48, 7 × 9 = 63, 6 × 7 = 42, 8 × 9 = 72, 4 × 7 = 28, 6 × 9 = 54, 3 × 8 = 24. None of them has a neat digit pattern to lean on, which is exactly why they need drilling rather than reciting.
All twenty tables are written out in full, from the 1 times table to the 20 times table, each with the patterns hiding inside the row and the two or three facts that slow people down.
Anchors are the fastest way in. The 1, 2, 5 and 10 steps of any table come almost free, and every other fact in that row is one addition or one subtraction away from an anchor. Building from anchors beats counting up from the start of the row, because it works when the facts arrive out of order — which is how they arrive in real arithmetic.
Every perfect square up to 25² has a page, along with the non-square values people most often look up. Each shows the exact or rounded root, the working, the nearest squares either side, and how to bracket a root in your head.
Squares and roots are the same fact read in opposite directions, so learning them together halves the work: knowing 12 × 12 = 144 is the same as knowing √144 = 12.
Reading an answer is not learning it. Recall improves with the number of times a fact is retrieved under a little pressure, which is why every page here ends in a drill rather than a summary.
Sixty seconds a day, shuffled, beats twenty minutes once a week. The arcade has timed arithmetic drills, a times-tables sprint and a mental addition game, all free, all instant, and none of them asking for an account.
Learn the 1, 2, 5 and 10 anchors of each row first, then build every other fact by adding or subtracting one lot. Drill shuffled rather than in order, for a minute a day, checking each answer immediately.
The middle of the grid causes the most trouble because it has no digit pattern to lean on: 7 × 8 = 56, 6 × 8 = 48, 7 × 9 = 63, 6 × 7 = 42, 8 × 9 = 72. Drill those on their own rather than inside a full row.
Not to get by, but the 13 to 20 rows are quick once you split them: 17 × 6 is 10 × 6 plus 7 × 6. Learning the split is more useful than memorising eight extra rows.
A calculator answers the question you already know how to ask. Mental arithmetic is what lets you notice an answer is wrong, estimate before committing, and keep a longer calculation moving without stopping to type.
No. Every page and every drill here is free, instant, and works without signing in or giving an email address.
Start with the multiplication chart if you want the whole grid on one screen, pick a times table and drill it, or read how to learn the times tables without chanting.