A times table is just a list of multiples — the 2s, the 5s, the 10s, and so on. The 4 times table, for example, is

That is exactly skip counting by 4, written down once so you can remember it. Each number in the list is one more group of 4, so a table is the answers to 4\times 1,\ 4\times 2,\ 4\times 3,\ \dots all in a row. Press play: a marker hops along the number line, landing on each multiple and reading it aloud.

Now pick a number and skip-count it all the way to twelve times. Each step adds one more group — just like the hops above — and the last cell is n \times 12.

It sounds like a lot to learn, but two friends cut the work in half. First, order does not matter when you multiply:

This is called commutativity. Because 7\times 3 and 3\times 7 give the same answer, every fact you learn is really two facts — so you only have to learn about half of the whole table.

Here's the whole table at once. Slide a row and a column — where they cross is \text{row} \times \text{column}. Now swap the two sliders: you land on a different square, but the same answer, because a \times b = b \times a. The table is a mirror image across its diagonal — that symmetry is commutativity.

And second, some tables follow easy patterns you can spot in a moment:

• Times 10: just add a zero — 7\times 10 = 70.
• Times 5: the answer always ends in 0 or 5 — 5, 10, 15, 20, \dots
• Times 2: just double the number — 2\times 8 = 8 + 8 = 16.

Learn the patterns, lean on commutativity, and the times tables shrink from a scary wall of numbers into a handful of friendly tricks.

Khan Academy walks through the multiplication tables here: