rational number
1. 1
Positive and negative numbers
Numbers preceded by a minus sign "-"other than 0 are called negative numbers (negative numbers
Number).
Contrary to the meaning of negative numbers, numbers other than 0 are called positive numbers (positive
Number) (sometimes add "+"before the positive number as needed.
1.2
rational number
Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.
Integers and fractions are collectively called rational numbers (rational
Number).
Numbers are usually represented by points on a straight line, which is called the number axis ($ NUMBER
Axis).
Three elements of number axis: origin, positive direction and unit length.
Take any point on a straight line to represent the number 0, and this point is called the origin.
Numbers with only two different signs are called opposites.
Number). (Example: The reciprocal of 2 is-2; The reciprocal of 0 is 0)
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.
Value), recorded as |a|.
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. Two negative numbers, the larger one has the smaller absolute value.
1.3
Addition and subtraction of rational numbers
Rational number addition rule:
1. Add two numbers with the same sign, take the same sign, and then add the absolute values.
2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0.
When a number is added with 0, it still gets this number.
Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.
1.4
Multiplication and division of rational numbers
Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.
Two numbers whose product is 1 are reciprocal.
Rational number division rule: dividing by a number that is not equal to 0 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 0 by any number that is not equal to 0 to get 0.
mì
The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is called the base.
Number), n is called exponent.
The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0.
Scientific counting method is used to express numbers greater than 10 as the n power of a× 10.
From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.
Numbers).
chapter two
One-dimensional linear equation
2. 1
From Formula to Equation
An equation is an equation with unknowns.
All equations contain only one unknown (element) X, and the exponent of the unknown X is 1 (degree). Such an equation is called a linear equation with one variable.
equation
along with
one
Unknown).
Solving the equation is to find the value of the unknown quantity that makes the left and right sides of the equation equal, and this value is the solution of the equation.
Properties of the equation:
1. Add (or subtract) the same number (or formula) on both sides of the equation, and the result is still the same.
2. Both sides of the equation are multiplied by the same number, or divided by the same number that is not 0, and the results are still equal.
2.2
Starting from the Ancient Algebra Books —— On the Linear Equation of One Variable (1)
Moving the sign of the term on one side of the equation to the other side is called moving the term.
chapter three
A preliminary understanding of graphics
3. 1
Color graphics
Geometry is also called solid for short. What surrounds the body is the surface.
3.2
Line, ray, line segment
Axiom of line segment: Of all the connecting lines between two points, the line segment is the shortest (the line segment between two points is the shortest).
The length of the line segment connecting two points is called the distance between these two points.
3.3
Angle measurement
1 degree =60 points
1 min =60 seconds
1 fillet =360 degrees.
1 flat angle = 180 degrees
3.4
Comparison and operation of angles
If the sum of two angles is equal to 90 degrees (right angle), they are said to be complementary.
Angle), that is, each angle is the complementary angle of another angle.
If the sum of two angles is equal to 180 degrees (flat angle), the two angles are said to be complementary.
Angle), that is, each angle is the complement of another angle.
The complementary angles of equal angles (same angles) are equal.
The complementary angles of equal angles (same angles) are equal.
chapter four
Collection and arrangement of data
Collecting, sorting, describing and analyzing data is the basic process of data processing.
The above is the foundation, others need to use their own knowledge to answer questions!