Concept. Formula. Law Application Examples -- Junior High School Mathematics: Junior High School Mathematics

Author: Gong Dongmei
Publisher:
Publish Date: 2002-05-01
Features: "Examples of the Application of Concepts, Formulas, and Laws in Junior High School Mathematics" is compiled according to the requirements of the newly issued Full-Time Secondary School Mathematics Teaching Syllabus by the National Education Commission. It closely aligns with the content of the current unified textbooks for this subject, catering to the practical needs of the syllabus and the examination guidelines for the college entrance examination. The book covers all key knowledge points of the subject, including relevant graphs, tables, and the application scope, precautions, etc., of formulas and laws. It provides a comprehensive introduction to common errors, their corrections, and memory techniques. Additionally, each important and difficult-to-understand knowledge point is paired with typical examples for analysis, offering demonstrations to aid understanding and mastery, thereby enhancing problem-solving skills.
Chapter: Preliminary Knowledge of Algebra – Concepts, Formulas, and Laws [Algebraic Expressions]
An algebraic expression refers to a combination of numbers and letters connected by basic operation symbols (operations include addition, subtraction, multiplication, division, as well as exponentiation and root extraction learned later). A single number or a single letter is also considered an algebraic expression.
[Writing Notes for Algebraic Expressions]
1. When multiplying a number by a letter, the number should be written before the letter, and the multiplication sign is usually omitted. If the number is a fraction, it should be converted to an improper fraction.
2. When multiplying letters, the order of the letters is generally followed, and the multiplication sign is often omitted.
3. When multiplying numbers by each other, the multiplication sign should not be omitted.
4. In algebraic expressions involving division, it is generally written in fractional form.
[Writing Algebraic Expressions]
To write an algebraic expression is to represent simple quantitative terms using algebraic expressions.
[Value of an Algebraic Expression]
The result obtained by substituting numerical values for the letters in an algebraic expression and performing the operations as specified is called the value of the algebraic expression.
[Equation]
An equation is a statement containing an unknown number, such as \(2x + 3 = 37\).
[Solution of an Equation]
The value of the unknown that makes both sides of the equation equal is called the solution of the equation.
[Solving an Equation]
The process of finding the solution of an equation is called solving the equation.