Corresponding thing
(1) The concept of antipodal: Only two numbers with different symbols are called antipodal.
(2) The meaning of opposites: It is understood that opposites appear in pairs and cannot exist alone. From the number axis, except 0, the two numbers are opposite, on both sides of the origin, and the distance from the origin is equal.
(3) Simplification of multiple symbols: No matter the number of "+",the odd number of "﹣" is negative and the even number of "﹣" is positive.
(4) Summary of conventional methods: The way to find the reciprocal of a number is to add "﹣" in front of this number. For example, the reciprocal of A is ﹣a, and the reciprocal of m+n is ﹣(m+n). At this time, m+n is a whole. When you put a minus sign before an integer, use parentheses.
Mixed operation of rational numbers
(1) rational number mixed operation order: calculate the power first, then multiply and divide, and finally add and subtract; Operations at the same level should be calculated from left to right; If there are brackets, do the operation in brackets first.
(2) When performing the mixed operation of rational numbers, pay attention to the application of various operation rules to simplify the operation process.
Four operation skills of mixed operation of rational number and normal method
1. conversion method: first convert division into multiplication; Second, multiplication is converted into multiplication; Thirdly, in the mixed operation of multiplication and division, decimals are usually converted into fractions for reduction calculation.
2. Rounding method: In the mixed operation of addition and subtraction, two numbers with zero sum, two numbers with the same denominator, two integer products and two integer products are usually combined to solve.
3. Split method: first split the band score into the sum of an integer and a true score, and then calculate it.
4. Clever use of arithmetic: Clever use of addition arithmetic or multiplication arithmetic in calculation will often make the calculation easier.
Solve a linear equation with one variable
(1) General steps to solve a linear equation with one variable:
Removing the denominator, removing brackets, moving terms, merging similar terms, and converting the coefficient into 1 are just the general steps to solve the linear equation with one variable. According to the characteristics of the equation, all the steps are to gradually transform the equation into the form of x = a.
(2) When solving a linear equation with one variable, first observe the form and characteristics of the equation, and generally remove the denominator; If there are both denominators and brackets, and the denominator can be eliminated after the items outside the brackets are multiplied by the items inside the brackets, the brackets should be removed first.
(3) When solving an equation similar to "ax+bx=c", the left side of the equation should be merged into a term (a+b)x=c, so that the equation can be gradually transformed into the simplest form of ax=b to reflect the idea of reduction. When the coefficient of ax=b is converted into 1, it should be calculated accurately. Once the equation is clearly solved, it is necessary to accurately judge the sign, in which the same sign X of A and B is positive and the different sign X of A and B is negative.
The above is the essence of my notes for you. For reference only, I hope it will help you.