In ancient China, multiplication was carried out by several chips. There are three layers in calculating multiplication: the upper layer is the multiplicand, the middle layer is the product and the lower layer is the multiplier. Multiply the multiplicand by the largest bit of the multiplier, remove the calculation of this bit after multiplication, multiply it by the second bit, and add the numbers on the corresponding bits of the two products until the multiplication is over. For example, 8 1 × 8 1, first put the multiplier and the multiplicand in the high position and the low position respectively, as shown in Figure (a). Multiply 80 by 8 1 to get 6480. When "8" is used up, it will be discarded, as shown in Figure (b). 8 1 times 1 to get 8 1, plus 6480, it is equal to 656 1. When "1" is used up, put it down and get Figure (c).
﹝a﹞﹝b﹞﹝c﹞
The level of calculation is to change multiple digits into single digits, multiply multiple digits, multiply one digit and add one digit. The basic principle is exactly the same as the general pen multiplication now, but the order of using multipliers is opposite to the current practice.
In the Middle Ages, several practical and interesting multiplications were popular in India. Cross multiplication is one of them, and Indians call it lightning multiplication. Such as 325 × 478 = 155350.
1494, the Italian mathematician Bacceli (1445- 15 14) introduced eight kinds of multiplication. The first multiplication is exactly the same as the commonly used pen multiplication, and the sixth multiplication is grid multiplication. This method was introduced to China in the15th century, and it is also called tapestry because of its graphic resemblance to tapestry (see the figure below).
If we carefully analyze the above table (even compare the algorithms of cross multiplication), we can appreciate the ingenuity of these multiplications.
The ingenious calculation of multiplication is used, such as:12×15 =12×10+5×10+2× 5.
Nowadays, people generally describe those who are good at calculating, calculating and planning as having a "career" in mind.