One,

Knowledge carding

Knowledge point 1: the concepts of positive numbers and negative numbers: we call numbers such as 3, 2, +0.5 and 0.03% positive numbers, all of which are numbers greater than 0; For example, -3, -2, -0.5,

-0.03% is called a negative number. Are all numbers less than 0. 0 is neither positive nor negative. We can use positive numbers and negative numbers to represent quantities with opposite meanings.

Knowledge point 2: the concept and classification of rational numbers: integers and fractions are collectively called rational numbers. There are two main classifications of rational numbers:

Note: Both finite decimals and infinite cyclic decimals can be regarded as fractions.

Knowledge point 3: the concept of number axis: the straight line defining the origin, positive direction and unit length as follows is called number axis.

Knowledge point 4: the concept of absolute value:

( 1)

Geometric meaning: the distance from the point representing a on the number axis to the origin is called the absolute value of the number a, and it is recorded as | a |.

(2)

Algebraic significance: the absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of zero is zero.

Note: The absolute value of any number is greater than or equal to 0 (i.e. non-negative).

Knowledge point 5: the concept of reciprocal:

( 1)

Geometric meaning: the number represented by two points on the number axis is located on both sides of the origin, and the distance from the origin is equal, which is called reciprocal;

(2)

Algebraic significance: Two numbers with different signs but equal absolute values are called reciprocal. The antonym of 0 is 0.

Knowledge point 6: Comparison of rational numbers:

The basic principle of rational number size comparison: all positive numbers are greater than zero, all negative numbers are less than zero, and positive numbers are greater than negative numbers.

Comparison of rational numbers on the number axis: the number on the right is always greater than the number on the left.

Comparison between rational number and absolute value: two positive numbers, the positive number with larger absolute value is larger; Two negative numbers, the negative number with larger absolute value is smaller.

Knowledge point 7: rational number addition rule:

(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;

(2) When two numbers with different signs are added and the absolute values are equal, the sum is 0; When the absolute values are not equal, take the sign of the addend with larger absolute values and subtract the addend with smaller absolute values from the addend with larger absolute values;

(3) Adding a number to 0 still gets this number.

Knowledge point 8: rational number addition algorithm:

Additive commutative law: When two numbers are added, the position of the addend is reversed and the sum remains the same.

Law of addition and association: when three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged.

Knowledge point 9: rational number subtraction rule: subtracting a number is equal to adding the inverse of this number.

Knowledge point 10: rational number addition and subtraction mixed operation: according to the law of rational number subtraction, all addition and subtraction operations can be unified into addition operations, and then brackets and plus signs are omitted, and calculations are made by using the law of addition and the law of addition operation.