MindMap Gallery Primary School Mathematics-050 Numbers and Algebra Mind Map of Formulas and Equations
Primary school mathematics general review of numbers and algebra: mind map of formulas and equations, including using letters to represent numbers, equations, solving equations, etc.
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Numbers and Algebra: Formulas and Equations
Use letters to represent numbers
meaning of numbers
Using letters to represent numbers can express quantitative relationships concisely, and can also express the results of operations.
Number writing (or abbreviation)
In expressions containing letters, the multiplication sign between numbers and letters, or between letters and letters, can be recorded as "•" or omitted. When the multiplication sign is omitted, the numbers should be written in front of the letters. For example, 6×a=6•a=6a.
When expressing a division equation using an expression containing letters, the calculation result should be written in the form of a fraction.
When 1 is multiplied by any letter, both the 1 and the multiplication sign can be omitted.
When two identical letters are multiplied, they can be written as the square of the letter; when several different letters are multiplied. The writing results are generally arranged in alphabetical order. a×b=a² (pronounced a squared), a×b×c=abc
Common applications
express quantitative relationship
Express the laws of operations and properties of operations
Use letters to express calculation formulas
Substituting numerical values into equations to evaluate
First write out what number the letters equal, then write out the original formula, and then substitute the numerical values into the original formula to evaluate. (When substituting data into the equation to evaluate, the omitted multiplication sign in the original equation must be restored).
When the letters contained in the same formula take on different numerical values, the values of the formula obtained are generally also different.
equation
The meaning of the equation
The meaning of the equation
Expressions expressing equality are called equations.
The meaning of the equation
An equation containing unknown numbers is called an equation. Two conditions must be met: first, it must be an equation, and second, it must contain unknown numbers.
The relationship between equations and equations
All equations are equations, but equations are not necessarily equations.
Conditions that the equation satisfies: equation, unknowns
Solving equations
Solutions to EquationsSolutions to Equations
Solution of the equation
The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation
Solving equations
The process of finding the solution to an equation is called solving the equation.
basis for solving equations
The relationship between the various parts of the four arithmetic operations
Properties of equations
Property 1: If the same number is added or subtracted from both sides of the equation, the left and right sides are still equal.
Property 2: If both sides of the equation are multiplied by the same number or divided by the same number that is not 0, the left and right sides are still equal.
Format for solving equations
First write the word "Jie", then add a colon ":". In the process of solving equations, write one equation in each line, the unknowns are written on the left side of the equation, and the equal signs of the equations in each line should be aligned.
Solve word problems using equations
significance
Solving word problems using equations is to use letters to represent unknown numbers in actual problems, and list equations containing unknown numbers based on equivalence relationships. That is, an equation, and then solving the equation to get the correct answer to the word problem.
step
1. Understand the meaning of the question, find the unknown number, and represent it with the letter x;
2. Analyze the equivalence relationships in practical problems and list equations based on the equivalence relationships;
3. Solve the equation and check your answer.
Precautions
Find the solution without writing the name of the actual unit after it.
Check whether the solution obtained meets the requirements of the question or the actual situation.
Enjoy it
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