Basic properties of fractions (concepts and basic properties of fractions and fraction equations)
Knowledge]
【Thinking method】
1. Change concepts
Reduction is an important mathematical thinking method, which is widely used. It can transform complex problems into simple ones, and unfamiliar problems into familiar ones. Many places in this chapter reflect the idea of transformation, such as division of fractions and multiplication of fractions. The basic idea of fractional addition and subtraction: addition and subtraction of fractions with different denominators and addition and subtraction of fractions with the same denominator; the basic idea of solving fractional order equations is to convert fractional order equations into integral equations, so as to obtain the solution of fractional order equations.
2. Modeling ideas
The commonly used mathematical methods in this chapter of Youyou Resource Network include: factorization, general division, approximate division, denominator removal, etc. When using mathematical knowledge to solve practical problems, you must first establish a simple mathematical model, solve practical problems through the mathematical model, and experience the mathematical process of “practical problem-fractional equation model-solution-explain the rationality of the solution” and experience the fractional equation Model thinking to understand theoretical and practical issues.
3. Similarity
This chapter highlights the method of analogy. Deduce the basic properties, approximate division, general division and algorithm analogy of fractions from the basic properties of fractions, approximate division of fractions, general division and algorithm analogy, deduce some calculation skills of fractions from the analogy of some calculation skills of fractions, Both reflect the importance of analogy. A Better Resource for Fractional Equations *** Solutions and applications can also be compared to linear equations in one variable.