Rod Calculus - Multiplication

Multiplication

Sun Tzu described in detail the algorithm of multiplication in The Mathematical Classic of Sun Zi. On the right are the steps to calculate 38×76:

1. Place the multiplicand on top, the multiplier on bottom. Line up the units place of the multiplier with the highest place of the multiplicand. Leave room in the middle for recording.
2. Start calculating from the highest place of the multiplicand (in the example, calculate 30×76, and then 8×76). Using the multiplication table 3 times 7 is 21. Place 21 in rods in the middle, with 1 aligned with the tens place of the multiplier (on top of 7). Then, 3 times 6 equals 18, place 18 as it is shown in the image. With the 3 in the multiplicand multiplied totally, take the rods off.
3. Move the multiplier one place to the right. Change 7 to horizontal form, 6 to vertical.
4. 8×7 = 56, place 56 in the second row in the middle, with the units place aligned with the digits multiplied in the multiplier. Take 7 out of the multiplier since it has been multiplied.
5. 8×6 = 48, 4 added to the 6 of the last step makes 10, carry 1 over. Take off 8 of the units place in the multiplicand, and take off 6 in the units place of the multiplier.
6. Sum the 2380 and 508 in the middle, which results in 2888, the product.