Cross multiplication is particularly convenient for solving some proportional problems. However, if it is used improperly, it will make mistakes.

(1) principle introduction

An example is given to illustrate this principle.

The average score of students in a class is 80, including 75 for boys and 85 for girls.

Find the ratio of male to female students in this class.

Method 1: Funny (and efficient) method. One male and one female, with a total score of 160 and an average score of 80.

Points. The ratio of male to female students is 1: 1.

Method 2: Assume that boys have A and girls have B.

(A*75+B85)/(A+B)=80

After finishing, A=B, so the ratio of male to female students is 1: 1.

Method 3:

Boys: 75 5

80

Girl: 85 5

Boys: girls = 1: 1.

Individuals in a set have only two different values, some of which are A and the others are B. ..

The average value is c, and the ratio of individuals with a value to individuals with b value is found. Suppose a has x and b has (1-X).

AX+B( 1-X)=C

X=(C-B)/(A-B)

1-X=(A-C)/A-B

Therefore: x: (1-x) = (c-b): (a-c)

The above calculation process can be abstracted as follows:

A C-B

C

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This is called cross multiplication.

Cross multiplication should pay attention to the following points when using:

The first point: it is used to solve the proportional relationship between the two.

The second point: the obtained proportional relationship is the proportional relationship of cardinal number.

The third point: put the total average in the middle, on the diagonal, reduce the large number and put the result on the diagonal.