First, understand two laws.
1, rational number addition rule:
Add two numbers with the same sign, take the same sign, and then add the absolute values. Add two numbers with different signs, and when the absolute values are equal, the sum is 0; When the absolute values are not equal, take the sign of the addend with the larger absolute value and subtract the smaller absolute value from the larger absolute value.
When a number is added to 0, it still gets the number.
According to the description of the addition law of rational numbers, when adding rational numbers, we should first judge the type of addition, that is, the addition of two numbers with the same sign, the addition of two numbers with different signs, or whether an addend is 0. Then act according to the law. In order to avoid mistakes, the principle of "sign first, then value" can be adopted in calculation, that is, the sign of sum is determined according to the law, and then the value of sum is calculated. Among them, the numerical value is determined by subtracting the smaller absolute value from the larger absolute value, rather than subtracting the smaller absolute value from the larger absolute value.
Second, master two algorithms.
Additive commutative law's and elementary school's law of addition still applies within the scope of rational numbers.
Additive commutative law;
Additive associative law:
When adding and subtracting rational numbers, if the algorithm can be used reasonably and skillfully according to the characteristics of the topic, the calculation will become simple and easy to solve.
Third, rational number addition and subtraction mixed operation
The basic steps of rational number addition and subtraction mixed operation are as follows: if it can be converted into addition, then the original mixed operation will be unified into addition operation, and the formula can be regarded as the sum of several positive numbers and several negative numbers. The above formula can also be written as the sum of omitting the plus sign, that is, if "+"and "-"are regarded as attribute symbols, they can be read as the sum of,, and; If "+"and "-"are regarded as operation symbols, they can be read as minus 5 minus 9 plus 7 plus 2. Then, combined with the algorithm, the result can be simplified.
Pay attention to the addition and subtraction of rational numbers:
① When exchanging the positions of addends, they should be exchanged with symbols.
② When adding and subtracting rational numbers, don't calculate blindly, pay attention to the characteristics of the topic, and use the algorithm appropriately to achieve the purpose of simplification.
③ The sum of rational numbers can be greater than or less than any addend. It can be positive or negative.