Law of rational number addition
(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;
⑵ Add two numbers with different symbols whose absolute values are not equal, take the sign of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value; (3) The sum of two mutually opposite numbers is zero; (4) Add a number to zero and you still get this number.
2. Arithmetic of rational number addition (1) additive commutative law: a+b = b+a.
⑵ law of additive combination: (a+b)+c=a+(b+c)
Multiplication rule of rational numbers
Rule 1: multiply two numbers, the same sign is positive and the different sign is negative, and the multiplication takes the absolute value; ("The same sign is positive and the different sign is negative" refers to the situation of "multiplying two numbers". If there are more than two factors, Rule 3 must be applied. Rule 2: Any number multiplied by 0 will get 0; Rule 3: Multiply several numbers that are not 0. When the number of negative factors is even, the product is positive. When the number of negative factors is odd, the product is negative; Rule 4: Multiply several numbers. If one of the factors is 0, the product is equal to 0.
Multiplication algorithm of rational numbers
(1) Multiplication commutative law: Generally speaking, in rational number multiplication, two numbers are multiplied, and the position of the commutative factor is equal to the product. Namely ab=ba
⑵ Law of Multiplication: When three numbers are multiplied, the first two numbers are multiplied or the last two numbers are multiplied, and the products are equal. That is, (ab) c = a (BC). (3) Multiplication and distribution law: Generally speaking, the multiplication of a number with the sum of two numbers is equivalent to the multiplication of this number with these two numbers respectively, and the products are added. That is, a(b+c)=ab+ac.
Matters needing attention in the power law of rational numbers in mathematics
1. Power is an operation. Equivalent to "+,-,×,". Teachers should make students understand this point when teaching, and at the same time ask students to master the writing method and format. Emphasizing the meaning of power is the same as "sum, difference, product and quotient". If the result is 8. So the power is 8. For example, 2×4, 2×4=8. So we can't say that 8 is a power, but that 23 is a power of 8. At the same time, emphasis has two meanings, not only referring to the multiplication of n a, but also representing the operation result of power.
Secondly, in the teaching of rational number power, we mainly emphasize its operation, so we pay special attention to the teaching of rational number power sign law. The rule is: any power of positive number is positive, any power of 0 is positive, it is 0, the positive power of negative number is negative, and the even power of negative number is positive. In teaching, when doing power, the teacher emphasizes that the sign should be determined before calculation, for example, =4.
The above is the power law of rational numbers in the first grade mathematics that I sorted out for you.