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The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. [2] "Table of Pythagoras" on Napier's bones [3] The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC).
One of the main properties of multiplication is the commutative property, which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3: 4 × 3 = 3 + 3 + 3 + 3 = 12. {\displaystyle 4\times 3=3+3+3+3=12.}
so 3 × 17 = 30 + 21 = 51. This is the "grid" or "boxes" structure which gives the multiplication method its name. Faced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented:
A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).
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