1, rational number multiplication rule:

Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value. That is to say, if two numbers are both positive or negative, then their product is also positive; If one number is positive and the other number is negative, then their product is negative. At the same time, if any number is multiplied by 0, the product is still 0. This rule can be expressed by letters: (a/b)×(c/d)=(ac)/(bd).

For example, if we calculate (-3)×4, the result can be-12 according to the multiplication rule of rational numbers. Because the signs of -3 and 4 are different, the result should be negative, and |-3|×|4|=3×4= 12, so (-3) × 4 =

2, rational number division rule:

Divide two rational numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide 0 by any number except 0 to get 0. This rule can be expressed in letters: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(BC).

For example, if we calculate (-8)÷2, the result can be -4 according to the division rule of rational numbers. Because the signs of -8 and 2 are different, the result should be negative, and |-8 |⊙| 2 | = 8÷2 = 4, so (-8) ÷ 2 =-. Similarly, if you divide 0 by any number other than 0, you get 0, for example, 0÷(-7)=0.

The difference between rational number and irrational number:

1, with different definitions: rational numbers are the collective name of integers and fractions, and all rational numbers can be converted into component numbers; Irrational numbers cannot be written as the ratio of two integers, nor can they be converted into the form of component quantities.

2. Different in nature: rational numbers are closed, dense, sequential, transitive, additive and multiplicative; Irrational numbers do not have these properties. For example, for any two rational numbers, their sum, difference, product and quotient (divisor is not 0) are still rational numbers, but they are not necessarily true for irrational numbers.

3. Different ranges: rational numbers include integers and fractions, and the range is smaller than irrational numbers. All rational numbers can be expressed as finite decimals or infinite cyclic decimals, while irrational numbers can only be expressed as infinite acyclic decimals. For example, root number 2 and root number 3 are irrational numbers and cannot be written in the form of finite decimal or infinite cyclic decimal.