First, the cross multiplication formula
Cross left multiplication equals quadratic coefficient, right multiplication equals constant term, and cross multiplication plus equals linear coefficient.
Second, the use of cross multiplication.
Fast calculation of 1. multiplication: When it is necessary to calculate the multiplication of two large multi-digits, cross multiplication can simplify the calculation process and reduce the possibility of errors.
2. Multiplication similar to monomial: In algebra, cross multiplication can also help to calculate multiplication similar to monomial, especially for expressions with variables, such as polynomial multiplication.
3. Teaching aid: Cross multiplication can be used as a teaching aid to introduce and demonstrate the calculation method of multi-digit multiplication to help students understand and master this concept.
To use cross multiplication, we first need to decompose the two multipliers into different digits, such as 1, 10, 100 digits, and then cross multiply. Then the results of cross multiplication are accumulated according to the corresponding digits, and finally the final product result is obtained.
It should be noted that cross multiplication is suitable for simple multiplication calculation, and more complicated multiplication or multiplication with decimals may require other more accurate and complicated calculation methods. Usually, when carrying out multiplication calculation, you can choose the method that suits you, including standard vertical calculation method, distribution method and other commonly used multiplication calculation methods.
Third, the origin of cross multiplication
Cross multiplication, also known as Gelosia multiplication or Gelosia lattice, can be traced back to Italy in the 3rd century A.D./Kloc-0 and was invented by a mathematician named Giovan Battista della Guelphi Guelph. He is an aristocrat in Florence, Italy, and also a math teacher and scholar.
In his book, George described Geppen multiplication, which was named after his surname. He invented this method to simplify multiplication, especially to deal with larger numbers. Giorgio's method makes the calculation of large number multiplication more intuitive and concise by means of cross multiplication, symmetry and staggered calculation.