Rational number multiplication and division is a basic operation skill in mathematics, which may be difficult for beginners. However, as long as we understand the concept and properties of rational numbers and master the rules of multiplication and division, we can easily carry out multiplication and division of rational numbers.

First, let's review the concept of rational numbers. A rational number consists of two integers, one is a numerator and the other is a denominator, where the denominator is not equal to zero. All rational numbers can be expressed in this form, for example: 1/2, -3/4, 0, etc.

Next, let's look at the properties of rational numbers. First of all, rational numbers are ordered, that is, they can be arranged in a certain order. Secondly, rational numbers can be added, subtracted, multiplied and divided, among which multiplication and division is the basic operation. In the multiplication and division of rational numbers, we need to follow the following rules:

The multiplication of rational numbers satisfies the commutative law and associative law, that is, ab=ba, (ab)c=a(bc). The multiplication of rational numbers satisfies the distribution law.

That is, a(b+c)=ab+ac. The multiplication of rational numbers satisfies the reciprocal property, that is, a number multiplied by its reciprocal is equal to 1. The division of rational numbers satisfies the reciprocal property, that is, a number divided by its reciprocal is equal to 1.

The multiplication and division of rational numbers satisfy special laws, such as 0 times any rational number equals 0, 1 times any rational number equals itself, any number divided by 1 equals itself, and any number divided by 0 equals infinity (in limit theory).

In practice, we can use various techniques to simplify the calculation process, such as simplification: if the numerator and denominator of a rational number have common factors, we can simplify it to simplify the calculation.

Decomposition: If a rational number needs to be multiplied, we can decompose it into multiple factorial multiplication forms to simplify the calculation.

Special case handling: For some special rational numbers, such as 0, 1,-1, etc. We need to master their multiplication and division rules.

In addition to the above skills, we can also use some tools to assist calculation, such as calculators and computer software. These tools can greatly reduce our calculation time and energy, and let us multiply and divide rational numbers more efficiently.

In a word, rational number multiplication and division is a basic operation skill in mathematics, and we need to master its basic laws and various skills to simplify the calculation process. In practical application, we can use some tools to assist calculation to improve efficiency. At the same time, we need to practice and consolidate constantly to deepen our understanding and mastery of rational number multiplication and division.