It is conditional what number or formula the letters in the score represent.
When the (1) score is meaningless, the value of the letters in the denominator makes the denominator zero, that is, when B=0, the score is meaningless.
(2) When the score is zero, it must be done on the premise that the score is meaningful, and the denominator value and the numerator value must be non-zero at the same time. These two conditions are indispensable.
(3) The score is meaningful, that is, the denominator in the score is not zero.
The basic properties of a fraction: both the numerator and denominator of the fraction are multiplied by (or divided by) the same algebraic expression that is not equal to zero, and the value of the fraction remains unchanged, which is expressed by the formula: AB=, AB=. (where m is an algebraic expression that is not equal to zero).
The three letters A, B and M in the fraction all represent algebraic expressions, in which B must contain letters, except that A can be equal to zero, and neither B nor M can be equal to zero, because if B=0, the fraction is meaningless; If M=0, multiplying or dividing by the denominator of the fraction will make the fraction meaningless.
Reduced scores and general scores of scores [source: subject network ZXXK]
(1) The concept of reduction: The common factor of the numerator and denominator of a fraction is called the reduction of the fraction.
(2) The basis of fractional reduction: the basic properties of fractions.
(3) Fraction reduction method: factorize the numerator and denominator of the fraction, and then remove the common factor of the numerator and denominator.
(4) simplest fraction's concept: When the numerator and denominator of a fraction have no common factor, it is called simplest fraction.
3. Fraction operation
1. Fraction addition and subtraction rules
(1) Total score: The process of converting scores with different denominators into scores with the same denominator is called total score [Source: Xue]. Part. Network z.x.x.k]
(2) The law of addition and subtraction of fractions with the same denominator: fractions with the same denominator are added and subtracted, the denominator is unchanged, and the numerator is added and subtracted.
(3) The law of addition and subtraction of scores of different denominators: the scores of different denominators are added and subtracted first, and then added and subtracted.
2. Simplification of scores [Source: Xue. Part. Network z.x.x.k]
The simplification of fraction is the same as the operation of fraction, and the basis, process and method of simplification are the same as the operation. The simplification of fractions is mostly a mixture of addition, subtraction, multiplication and division of fractions, and the results of simplification retain the simplest fractions or algebraic expressions.
3. Fractional elementary arithmetic
The order of elementary arithmetic operation of fractions is the same as that of four operations of fractions. Multiply first, then divide, and finally add and subtract. If there are brackets, count them first. Some problems need to be solved by multiplication distribution law first, and then the calculation is simpler.
4. Fractional equation
Fractional equation is one of the equations, and the equation with letters in the denominator is called fractional equation.
Solution of fractional equation
(1) Denominator {the two sides of the equation are multiplied by the simplest common denominator (the simplest common multiple: the lowest common multiple, the highest power of the same letter, the copy only contained in one denominator), and the fractional equation is transformed into an integral equation; If you meet the opposite number, don't forget to change the sign. (2) According to the steps of solving the integral equation (shift the term, remove the brackets if there are brackets, pay attention to the sign change, merge similar terms, and convert them into 1), and find out the unknown value; ③ Root test (root test is needed after finding the value of the unknown quantity, because in the process of transforming the fractional equation into the whole equation, the range of the unknown quantity is expanded, which may lead to the increase of roots).
When finding the root, substitute the root of the whole equation into the simplest common denominator. If the simplest common denominator is equal to 0, this root is an added root. Otherwise, this root is the root of the original fractional equation. If the root of the solution is an increasing root, the original equation has no solution.
The basic idea of solving the fractional equation is to turn the fractional equation into an integral equation, and the specific method is to "remove the denominator", that is, both sides of the equation are multiplied by the simplest common denominator, which is also the general idea and practice of solving the fractional equation.
Application of Fractional Equation
Fractional equation and integral equation are the same in solving application problems, so we should carefully examine the problems, find out the equations that reflect all the quantitative relations in the application problems, set the unknowns appropriately and list the equations. Different from integral equations, after solving the equations, there are two tests, one is to test whether it is root-increasing, and the other is to test whether it meets the meaning of the question.