In primary school textbooks, the rules of fractional multiplication and division are as follows:

? Fractional multiplication: the product of denominator multiplication is denominator, and the product of numerator multiplication is numerator. It can also be said that the numerator and denominator are multiplied separately to make their own numerator and denominator.

How to understand the law of fractional multiplication? The rectangular area formula and drawing can be used to make students understand that the product of denominator is to produce a new counting unit; Molecular multiplication is how many such counting units there are.

? Fractional division: Multiplying a number equals multiplying the reciprocal of this number. It can be found that the negative law of fractional multiplication and division is very inconsistent. Why did division become multiplication? But also multiplied by the reciprocal of the divisor. It is necessary for children to understand this.

Teacher Zhu Guorong from Zhejiang said in the lecture: In fact, the law of division and the law of multiplication of fractions are the same, and the law of multiplication is the multiplication of numerator and denominator respectively; The law of division is to separate the numerator from the denominator. For example: 63/100 ÷ 7/10 = 9/ 10, that is, divide 63 by 7,100 and then divide it by10 to get 9/10. This reflects the beauty and consistency of mathematics. Multiplication multiplies separately, division divides separately.

? But 5/8÷3/7? For the smooth division of numerator and denominator, the fraction can be properly deformed according to its basic properties. The numerator and denominator are multiplied by 3 and 7 respectively at the same time, and finally converted into 5× 3× 7/8× 3× 7 ÷ 3/7 = 5× 7/8× 3 = 5/8× 7/3.

? It turns out that multiplying a number is equal to multiplying the reciprocal of this number, which is the basic form after deformation. In other words, it is the normality of a series of deformed fractional divisions. It also abstracts the law of fractional division-the multiplication of a number is equal to the reciprocal of this number. (it's abstraction in abstraction. )