When you enter middle school and start to contact algebra, you will definitely ask: What's the difference between algebra and arithmetic? How can we learn algebra well in middle school? The first chapter of the textbook-the study of elementary algebra knowledge is to review, consolidate and improve the algebra knowledge learned in primary schools, and also to make some preparations for future study. Attention should be paid to the following aspects:

First, deeply understand the meaning of using letters to represent numbers.

The fundamental difference between algebra and arithmetic is that it introduces letters for operation. Representing numbers by letters is one of the basic ideas of algebra, and it is also a bridge from arithmetic to algebra.

Using letters to represent numbers can concisely express the laws and characteristics of things, which has the advantages of simplicity and universality. A+b=b+a represents the commutative law of addition, where A and B respectively represent any two numbers, so the number represented by letters is arbitrary; Once the number represented by a letter is determined, the number it represents is determined. For example, x+3 means all numbers greater than x by 3, but when x=5, x+3 means 8.

When using letters to represent numbers, we should pay attention to:

(1) For the same question, different numbers should be represented by different letters.

(2) When multiplying with letters, the "x" sign is usually omitted, for example, 3×a is written as 3a, and a×b is written as a*b or ab.

(3) In the product of numbers and letters representing numbers, numbers are generally written in front of the letters. If the number is decimal, it will become a false decimal, for example, xy×6 stands for 6xy, 1×m stands for m.

(4) In division with letters, it is generally written in fractional form, such as s \t writing, without \ symbol.

Second, master the evaluation method of column algebra and algebra.

Studying the construction, deformation and application of "formula" is an important content of middle school algebra, and algebraic formula is a relatively simple category in "formula".

Column algebra is to express the words related to quantity in the problem with formulas containing numbers, letters and operational symbols. When enumerating algebraic expressions, we should first read the stem carefully, analyze the quantitative relations involved in the stem clearly, and pay attention to the statements such as "big", "small", "many", "fraction" and "reciprocal" in algebraic expressions and the operational relations of addition, subtraction, multiplication and division. At the same time, we should understand the operation sequence and the use of parentheses.

The value of algebraic expression is determined by the value of letters in algebraic expression. When each letter in the algebraic expression takes a number, the algebraic expression also represents a number. In order to find the value of algebraic expression correctly, numerical substitution must be carried out correctly first. When directly replacing the evaluation, the following formula can be applied:

"Dig out the letters and replace them with numbers, and keep the numbers and symbols; Replace it with fractions or negative numbers and add parentheses. " Generally speaking, there are three steps to find the value of an algebraic expression:

(1) represents the numerical value expressed by letters in the algebraic expression;

(2) Copy the original formula and replace the letters in the original formula with the values expressed by letters;

(3) Calculate the formula and find the value of the algebraic formula.

Thirdly, it is very important to form the good habit of carefully examining questions and carefully completing every step of calculation and checking calculation, which is very important for successfully completing the learning task of middle school mathematics in the future.

Example 1 Fill in the blanks:

(1) If the side length of a square is acm, the perimeter of the square is _ _ ____cm and the area is _ _ _ _ cm2;

(2) The area of a rectangle is 100cm2, the length is (x+2)cm, so the width is _ _ _ _ _ cm;

(3) There are several math classes in a school, with an average of 47 students in each class, so there are _ _ _ _ students in the whole school; If * * * members account for 8% of the students in the whole school, then there are * * * members in the whole school.

(4) Company A has m employees, and the number of employees in Company B is twice as small as that in Company A 13, so Company B has _ _ _ _ _.

Solution: (1) 4a, a2; (2) ; (3) 47n，47×n； (4) (2m- 13).

Description:

(1) In the formula containing the multiplication of numbers and letters, the numbers should be multiplied and written in front of the letters, and the multiplication sign between the numbers is indicated by "×". (3) The result in the question should be written as 47× n instead of 47n* or 47n.

(2) When a formula containing addition and subtraction operations needs to be written in units, the whole formula should be enclosed in brackets. (4) In the question, Company B has employees (2m- 13), which cannot be written as 2m- 13.

Example 2 Multiple-choice questions (one out of four):

In the following formula, (A) mn÷3 (B) 4ab*3 (c) 2xy2 (D) stands for the correct method.

Solution: Choose (d).

Example 3 Tell the meaning of the following algebraic expression: (1) A2-B2; (2)(a+b)(a-b)； (3)(a+b)2； ⑷a-B2 .

Solution: (1)a2-b2 represents the difference between the squares of two numbers A and B;

(2) The meaning of (a+b) (a-b) is the product of the sum of two numbers A and B and the difference between the two numbers;

(3) The meaning of (A+B) 2 is the square of the sum of A and B;

(4)A-B2 means that A minus the square of B. ..

Example 4 Let the number of A be X, and the number of B be expressed by an algebraic expression: (1) The number of B is 3 larger than half the number of A; (2) The number B equals the reciprocal of the number A. ..

Solution: (1)+3; (2)。

Example 5 is represented by algebraic expression:

(1) The circumference of a square is lcm, so what is its area?

(2) The diameter of a small circle is the radius of a big circle. If the radius of the small circle is r, how many times is the area of the big circle?

Solution: (1) If the perimeter of a square is lcm and the side length is cm, the area of this square is () 2cm2；;

(2) If the radius of the small circle is r, the area is πr2, the radius of the big circle is 2r, and the area of the big circle is π(2r)2. The area of a big circle is four times that of a small circle.

Example 6 When a=3b and b=2c, the value of (where b≠0) is obtained. Solution: b=2c, a=3b, b≠0,

∴ a=6c, c≠0, when a=6c, b=2c, c≠0,

.

∴(b≠0) when a=3b and b=2c, =