* Numbers are represented by letters, which can concisely express the quantitative relationship and the result of operation.
2. Use letters to express common quantitative relations, operation rules and properties, and calculation formulas of geometric shapes.
(1) Common quantitative relations
The distance is represented by S, the speed V is represented by T, and the time is represented by T. The relationship between them is: S = VTV = S/T T = S/V.
The total price is represented by A, the unit price is represented by B, and the quantity is represented by C. The relationship between them is: A = BC B = A/C C C = A/B.
(2) Operating rules and characteristics
Additive commutative law: A+B = B+A.
Additive associative law: (a+b)+c=a+(b+c)
Multiplicative commutative law: ab=ba
Law of multiplicative association: (ab)c=a(bc)
Multiplication and distribution law: (a+b)c=ac+bc
The essence of subtraction: A-(B+C) = A-B-C.
(3) Formulas for expressing geometric shapes with letters.
The length of a rectangle is represented by a, the width by b, the circumference by c and the area by s: c=2(a+b) s=ab.
The side length a of a square is denoted by, the perimeter is denoted by c, and the area is denoted by s: c = 4as = a.
The base a of the parallelogram is denoted by, the height is denoted by h, and the area is denoted by s: s=ah.
The base of the triangle is represented by a, the height by h and the area by s: s=ah/2.
The upper bottom of the trapezoid is represented by a, the lower bottom by h, the center line by m and the area by s: s = (a+b) h/2; s=mh
A circle has a radius of r, a diameter of d, a circumference of c and an area of s: c = ∏ d = 2 ∏ r s = ∏ r.
The radius of the sector is denoted by R, n denotes the degree of the central angle, and the area is denoted by S: s=∏ nr/360.
The length of a cuboid is represented by A, the width by B, the height by H, the surface area by S and the volume by V: V = SHS = 2 (AB+AH+BH); v=abh
The side length of the cube is represented by a, the perimeter of the bottom surface is represented by c, the area of the bottom surface is represented by s, and the volume is represented by v: s = 6av = a.
The height of the cylinder is represented by H, the perimeter of the bottom surface is represented by C, the area of the bottom surface is represented by S, and the volume is represented by V: S side = CHs table =s side +2s bottom; v=sh
The height of the cone is represented by H, the bottom area by S, and the volume by V: v=sh/3.
3. How to write numbers with letters
When the number is multiplied by letters, letters and letters, the multiplication sign can be recorded as "."or omitted, and the number should be written before the letters.
When "1" is multiplied by any letter, "1" is omitted.
In a question, the same letter represents the same quantity, and different quantities are represented by different letters.
When the answer to a question is expressed by a formula containing letters, the divisor is usually written as the denominator. If there is a plus sign or a minus sign in the formula, the formula containing letters should be enclosed in brackets first, and then the company name should be written after the brackets.
4. Substitute the numerical value into the formula for evaluation.
* When substituting specific numbers into the formula for evaluation, pay attention to the writing format: write how many letters are equal to first, then write the original formula, and then substitute the numbers into the formula for evaluation. Letters represent numbers, and the unit name is not written after them.
* The letters contained in the same formula have different values, so the value of the formula is different.