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The table is split up into the nine columns. Here is how they're used:

 

For example, let's calculate 32 x 7 .

Lay out the two strips showing 3 and 2 at the top like this:

Two strips of the 3 and 2 times table laid out next to each other.

To multiply this number by 7, add the numbers along the diagonals of the seventh line, starting at the right:

Adding the diagonals of the two strips.

So the answer is 224 .