Properties of Mathematical Equations in Primary Schools
Adding or subtracting the same number on both sides of the equation at the same time, the result is still an equation; Both sides of an equation are multiplied or divided by the same non-zero number at the same time, and the result is still an equation. An equation with an equal sign is called an equation, and its properties are mainly used to solve the equation.
Property 1: Add (or subtract) the same algebraic expression on both sides of the equation, and the equation still holds.
If a=b, then a+c = b+c.
Property 2: When both sides of the equation are multiplied or divided by the same algebraic expression that is not 0, the equation still holds.
If a=b, there is a c = b c or a \c = b \c(c≠0).
Property 3: Equation is transitive.
If a 1=a2, a2=a3, a3=a4, then a 1=a2=a3=a4.
The nature of the equation is the basis of solving the equation, and many methods of solving the equation should be applied to the nature of the equation. If the term is shifted, the properties of the equation 1 are applied; Remove the denominator and apply Attribute 2 of the equation. By using the properties of the equation, when doing division, it should be noted that after conversion, the divisor cannot be 0, otherwise it is meaningless.
The difference between primary school mathematical formulas and equations refers to the formulas listed in the calculation of numbers or algebraic expressions, and the equations represent equations with equal relations. 2+3 is an expression, 2+3=5 is an equation and an expression. Formula: Calculate the result through four operations. Equation: It means that both sides of the equal sign have the same operation result. The equation should pay attention to 1. Formula: square of a+b =A square +2AB+b square.
An expression refers to an expression listed when calculating a number or an algebraic expression, and an equation represents an equivalent relationship. 2+3 is an expression, 2+3=5 is an equation and an expression. Formula: Calculate the result through four operations. Equation: It means that both sides of the equal sign have the same operation result.
What should be paid attention to in the equation?
1. formula: the square of a+b =A square +2AB+b square. For example: 3+4 square =3 square +2*3*4+4 square.
2. In the equation, you don't need to write a multiplication sign. Unknown number: X is usually set as unknown number, and other letters can be set, and all letters can be used. The unknowns of two equations in a problem cannot be the same!
3. The concept of "Yuan": During the Song and Yuan Dynasties, China mathematicians created "Tianyuan" to represent the unknown, and then established the equation. Later, people set up geographical elements, cultural elements and Thai elements to represent unknowns, and some elements are called multivariate equations. The representative work of this method is the Round Sea Mirror written by mathematician Ye Li (1248), in which "setting a Tianyuan" is equivalent to "setting an unknown x", so the unknown is called "yuan" when the equation is abbreviated now. For example, an unknown equation is called "unary equation". In ancient times, more than two unknowns were also called "Tianyuan", "Geo-element" and "Human element".
4. "Quadratic": The concept of quadratic in the equation is similar to algebraic expression. Refers to the sum of all unknown indicators in a project with unknown numbers. The term with the highest degree is the degree of the equation.
5. "Solution": the solution of the equation, also called the root of the equation. The value of an unknown quantity in an equation. Generally expressed as "x=a", where x represents an unknown number and a is a constant.
6. Solving the equation: refers to the process of finding the solution of the equation.