Rational number knowledge map
Operation knowledge of rational numbers-addition and subtraction of rational numbers.
The addition rule of (1) rational numbers;
(1) Two numbers with the same number are opposite, take the same symbol and add the absolute values;
(2) add two numbers with unequal absolute values, take the symbol with the largest absolute value, and subtract the one with the largest absolute value. Two opposite numbers add up to 0;
(3) Adding a number to 0 still gets this number;
(2) Arithmetic of rational number addition: ① additive commutative law: A+B = B+A; (2) Additive associative law: (a+b)+c=a+(b+c)
(3) the subtraction rule of rational numbers: subtracting a number is equal to adding the opposite number of this number; Namely: A-B = A+(-B);
Multiplication and division of rational numbers
(1) multiplication rule of rational numbers;
① Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;
② Any number multiplied by 0 is 0;
(2) Reciprocal: it still holds true in rational numbers, that is, two numbers whose product is 1 are reciprocal;
(3) The relationship between the sign of the product and the number of negative factors: several numbers that are not 0 are multiplied, and when the number of negative factors is even, the product is positive; When the number of negative factors is odd, the product is negative; Multiply several numbers, when a factor is 0, the product is 0;
(4) multiplication algorithm of rational numbers:
① Multiplicative commutative law: ab = ba
② Multiplicative associative law: (ab) c = a (BC);
③ Multiplication and distribution law: A (B+C) = AB+AC;
(5) the division rule of rational numbers: dividing by a number that is not 0 is equal to multiplying its reciprocal; Namely:
(6) Divide two numbers, the same sign is positive and the different sign is negative, and divide by the absolute value; Divide 0 by any number that is not 0 to get 0;
(7) In the mixed operation of addition, subtraction, multiplication and division of rational numbers, if there are no brackets, the operation will be carried out in the order of "multiplication and division first, then addition and subtraction";
Power of rational number
(1) power: the operation of the product of the same factor is called power, and the result of power is called power; (in n, a is the base and n is the exponent)
(2) Power algorithm of rational number:
① The odd power of a negative number is negative, and the even power of a negative number is positive;
② Any degree of a positive number is a positive number;
③ Any positive power of 0 is 0;
(3) The mixed operation order of rational numbers:
① Power first, then multiply and divide, and finally add and subtract;
② Operation at the same level, from left to right;
(3) If there are brackets, do the operation in brackets first, in the order of brackets, brackets and braces;
(4) Scientific notation: numbers greater than 10 are written in the form of a× 10n, where a is a number with only one integer. This notation is called scientific notation;
(5) Approximation accuracy: a divisor, rounded to this bit, indicating that the divisor is accurate to this bit.
(6) Effective Numbers: All numbers from the first non-zero number on the left to the precise digits are called the effective numbers of this divisor.
The above is the rational number of grade seven. All knowledge points are also a collection of test sites. This mode of summarizing knowledge points is: knowledge outline+knowledge points. Share the collection of knowledge points of integer addition and subtraction in the next issue.
Rational number knowledge points 1 rational number
Definition of rational number: positive integer 0 and negative integer are collectively called integers; Positive and negative scores are collectively referred to as scores. Integers and fractions are collectively called rational numbers.
2-axis
Definition of (1) number axis
In mathematics, numbers can be represented by points on a straight line, which is called the number axis and meets the following requirements:
1. Take any point on a straight line to represent the number 0, and this point is called the origin;
2. It is usually stipulated that a straight line is positive from the origin to the right and negative from the origin to the left;
3. Choose an appropriate length as the unit length, and take a point every other unit length from the origin to the right on the straight line, and then table 1, 2, 3, ... from the origin to the left, and express-1, -2, -3 in a similar way. ...
(2) Points on the number axis and rational numbers
Generally speaking, if a is a positive number, the point representing the number A on the number axis is on the right side of the origin, and the distance from the origin is one unit length; The point representing the number -a is on the left of the origin, and the distance from the origin is one unit length.
3 reciprocal
The concept of (1) inverse number
Like 3 and -3, 4 and -4, only two numbers with different symbols are called reciprocal.
Generally, a and -a are opposites, especially the inverse of 0 is 0. Here a stands for any number, which can be positive, negative or 0.
(2) Geometric significance
The two points corresponding to two mutually opposite numbers on the number axis are located on both sides of the origin, and the distance to the origin is equal; On the contrary, points located on both sides of the origin and at the same distance from the origin are represented by.
These two figures are opposite.
(3) the nature of reciprocal
Any number has a reciprocal, and there is only one. The reciprocal of a positive number must be negative; The reciprocal of a negative number must be a positive number; The antonym of 0 is still 0.
4 absolute value
Definition of (1) absolute value
Generally speaking, the distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, which is denoted as |al.
(2) the meaning of absolute value
The algebraic meaning of 1. absolute value: the absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.
That is, if a > 0, | a | = a
If a = 0, then | a | a | = 0；;
If a < 0, then | a | =-a.
2. Geometric meaning of absolute value: the absolute value of a number is the distance from the point representing this number to the origin. The farther away from the origin, the greater the absolute value; The closer to the origin, the smaller the absolute value.
(3) Nature of absolute value: absolute value is non-negative, that is, | a | ≥ 0; If the sum of absolute values of several numbers is 0, then each number is equal to 0, that is |a|+|b|+...+|m|=0, then a=b=...=m=0.
The above is the arrangement of some rational number knowledge points, hoping to help everyone.