Rational Numbers of Important Knowledge Points in Junior One Mathematics (1)
(1) Definition: A number consisting of integers and fractions. Include positive integer, 0, negative integer, positive fraction and negative fraction. Can be written as the ratio of two integers.
(2) Number axis: In mathematics, numbers can be represented by points on a straight line, which is called number axis.
(3) Inverse number: Inverse number is a mathematical term, which means that two numbers with equal absolute values and opposite signs are opposite to each other.
(4) Absolute value: Absolute value is the distance from a point corresponding to a number on the exponential axis to the origin. The absolute value of a positive number is itself, and the absolute value of a negative number is its inverse; The absolute value of 0 is 0, two negative numbers, the larger absolute value is smaller.
(5) Addition and subtraction of rational numbers
Add the same symbol to the same symbol and add the absolute values. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value.
(6) Multiplication of rational numbers
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Multiply any number by 0, and the product is 0. For example: 0× 1=0.
(7) Division of rational numbers
Dividing by a number that is not zero is equal to multiplying the reciprocal of this number.
Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide by 0
For any number that is not 0, you get 0.
(8) Power of rational number
The operation of finding the product of n identical factors is called power, and the result of power is called power. Where a is called the base and n is called the exponent. When a. When it is regarded as the result of the n power of A, it can also be read as "the n power of A" or "the n power of A"
(2) One-dimensional linear equation
Equation (1): first, let letters represent unknowns, and then write an equation containing unknowns according to the equation relationship, which is called an equation.
(2) One-dimensional linear equation
One-dimensional linear equation refers to an equation with only one unknown number, the highest order of which is 1, and both sides are algebraic expressions, which is called one-dimensional linear equation. Finding the value of the unknown quantity in the equation is called the solution of the equation.
(3) Properties of the equation
① Adding (or subtracting) the same algebraic expression on both sides of the equation is still valid.
If a=b
Then a+c=b+c
② Both sides of the equation are multiplied or divided by the same non-zero algebraic expression at the same time, and the equation still holds.
If a=b
Then there is a c = b c or a \c = b \c(c≠0).
③ The equation is transitive.
If a 1 = a2, a2 = a3, a3 = a4, ... an = an, then a 1 = a2 = a3 = a4 =...= an.
(3) Steps to solve the equation
The steps to solve a linear equation with one variable are: removing denominator, brackets, shift terms, merging similar terms, and converting unknown coefficients into 1.
(1) Denominator: Turn the coefficient into an integer.
(2) stent removal
③ Shift term: shift the sign of an item on one side of the equation to the other side.
④ Merge similar items.
⑤ The coefficient is 1.
(3) Inequality and unequal groups
(1) inequality
Using inequality symbols (
(2) the essence of inequality
① symmetry;
② Transitivity;
③ monotonicity of addition, that is, additivity of inequality in the same direction;
④ Monotonicity of multiplication;
⑤ Multiplicity of positive inequality in the same direction;
⑥ Positive inequalities can be multiplied;
⑦ Positive inequalities can be squared;
(3) One-dimensional linear inequality
A formula connected by an inequality symbol contains an unknown number whose degree is 1, whose coefficient is not 0, and whose left and right sides are algebraic expressions is called one-dimensional linear inequality.
(4) One-dimensional linear inequalities
The group of one-dimensional linear inequalities consists of several one-dimensional linear inequalities with the same unknowns.