Simplification and general points:

1. simplification: the common factor of the numerator and denominator of a fraction is simplified, and this deformation is called the simplification of the fraction;

Fractional reduction: The common factors in numerator and denominator are reduced, which is called fractional reduction. The basis of fraction reduction is the basic property of fraction, that is, the numerator and denominator of fraction are divided by the same algebraic expression that is not equal to zero, and the value of fraction remains unchanged. The reduction method and steps include:

(1) When both the numerator and denominator are monomials, the common factor is the product of the lowest power of the same factor and the greatest common divisor of the coefficient;

(2) When both the numerator and denominator are polynomials, the polynomial should be decomposed into factors and the common factors should be omitted.

2. Generalization: According to the basic properties of fractions, fractions with different denominators can be converted into fractions with the same denominator, which is called the generalization of fractions. Fraction general division: several fractions with different denominators are converted into fractions with the same denominator. This deformation is called the general division of fractions.

(1) When the denominators of several fractions are monomials, the simplest common denominator of each fraction is the least common multiple of the coefficient and the product of all different letters and the highest power of the same letter;

(2) If all denominators are polynomials, they should be arranged in descending or ascending order according to a certain letter, and then decompose the factors to find the simplest common denominator;

(3) The denominator of the divisible scores is the same, and the divisible scores are equal to the original scores respectively;

(4) General score and approximate score are two completely different variants. Approximate values apply to one fraction, while general fractions apply to multiple fractions. Simplifying a score is to simplify a score, and a general score is to simplify a score. note:

The reduction of (1) score and general score are based on the basic properties of the score;

(2) The sign-changing rule of the fraction: the numerator, denominator and symbol of the fraction itself have changed, but the value of the fraction remains unchanged.

(3) When dividing, the numerator and denominator are not products, so they cannot be reduced.

Main points of eighth grade mathematics knowledge

Operation of fraction: 1. Rules for addition and subtraction of scores:

(1) The fraction with the denominator is added and subtracted, and the numerator with the denominator is added;

(2) The addition and subtraction of fractions with different denominators are divided into fractions with the same denominator, and then calculated according to the addition and subtraction of fractions with the same denominator.

2. The law of multiplication and division of fractions: two fractions are multiplied, the product of molecular multiplication is the numerator of the product, and the product of denominator multiplication is the denominator of the product; Divide two fractions, invert the numerator and denominator of the divisor, and then multiply by the divisor.

4. The mixed operation order of fractions, first calculate the power, then calculate the multiplication and division, and finally calculate the addition and subtraction. If there are parentheses, calculate the inside of the parentheses first.

5. Fractional simplification evaluation questions pay attention to the problem-solving format. Simplify first, then evaluate the value of letters.

Common inspection methods

The operation of scores is usually a comprehensive examination of the knowledge of addition, subtraction, multiplication and division, reduction and factorization of scores, which is the focus of the senior high school entrance examination. Especially in the past two years, simplified evaluation has become a hot spot in the senior high school entrance examination. There are multiple-choice questions, fill-in-the-blank questions and calculation questions.

Misunderstanding reminder

(1) When the divisor is opposite, the minus sign is lost;

(2) Error caused by omission of multiplication operation when sharing;

(3) confuse the general score with the denominator, which is the general score, but throw away the denominator in the score;

(4) The calculation sequence is out of order, resulting in errors.

Eighth grade mathematics knowledge

Steps to solve application problems with column fractional equation;

The general steps of solving application problems with fractional equations are as follows:

(1) Setting the unknown: if the unknown required in the topic is directly represented by letters, it is called directly setting the unknown, otherwise it is called indirectly setting the unknown;

(2) Column Algebraic Formula: use algebraic formula containing unknowns to express the relevant quantities in the topic, and make schematic diagrams or tables when necessary to help straighten out the relationship between quantities;

(3) listing equations: listing equations according to the obvious or implied equation relationship in the topic;

(4) Solve the equation and test it;

(5) write the answer.

2. Matters needing attention in solving application problems with fractional equations:

Because using equations to solve practical problems is the answer to solve practical problems, we should consider the actual situation of the problem and leave out anything that is not practical, besides testing it from the mathematical aspect.

Common inspection methods

Solving application problems with fractional equation is a hot topic in senior high school entrance examination. The proposition is widely linked with practice, and the questions are novel and open. But as long as you master several steps of solving application problems by fractional equation, it is not difficult to solve them.

Misunderstanding reminder

(1) unit is not uniform;

(2) Ignore the "double check" after solving the fractional equation.