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MasterMath

Multiplication Table

The times table for any number, as far as you like, with the patterns that make it easier to remember.

The table

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The table—
Sum of all the results—
The last product—

The table

OperationResult

How this was worked out

    The rule

    n × 1, n × 2, n × 3 …

    Why it works

    A times table is repeated addition laid out in order. Each row is the previous one plus the number itself, which is why the table can be built without multiplying anything at all.

    How to do it by hand

    1. Start with the number itself
    2. Add it again for each row
    3. Doubling gives you × 2, × 4 and × 8
    4. × 10 is just the number with a zero on the end

    What is worth knowing

    The patterns do most of the work. The nine times table has digits that always add to nine, and it runs down on the tens and up on the units. The five times table alternates between ending in 0 and 5. The eleven times table repeats the digit up to 9. Knowing that multiplication is commutative also halves what there is to learn: 7 × 8 and 8 × 7 are one fact, not two, which cuts the hundred entries of a 10×10 table to fifty-five.

    Frequently asked questions

    What is the easiest way to learn times tables?

    Use the patterns. Doubling covers 2, 4 and 8; the nine table's digits always add to nine; ten just adds a zero.

    Why does commutativity help?

    Because 7 × 8 and 8 × 7 are the same fact. That halves the number of things to memorise.

    What is the pattern in the nine times table?

    The tens digit counts up while the units count down, and the two digits always add to nine.

    How far should the table go?

    Ten is the usual school target, twelve in some countries. Beyond that the patterns matter more than the memorising.