Using letters to represent numbers can express the quantitative relationship concisely, and can also represent 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 and the speed by t, and the relationship between them is as follows:
s=vt
v=s/t
T = signal-to-noise ratio
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 as follows:
A = BC
B = air conditioning
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 represented by, the perimeter is represented by c, and the area is represented by S.
c=4a
s=a2
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 a triangle is represented by a, the height by h and the area by s.
s=ah/2
The upper base of the trapezoid is represented by a, the lower base is represented by h, the center line is represented by m, and the area is represented by s.
s=(a+b)h/2
s=mh
The radius of a circle is represented by R, the diameter by D, the circumference by C and the area by S.
c=∏d=2∏r
s=∏r2
The radius of the sector is represented by r, n is the degree of the central angle, and the area is represented by s.
s=∏nr2/360
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=sh
s=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 s, and the volume is represented by v.
s=6a2
v=a3
The height of the cylinder is represented by H, the circumference of the bottom is represented by C, the area of the bottom is represented by S, and the volume is represented by V. 。
S side =ch
S table =s side +2s bottom
v=sh
The height of the cone is H, the bottom is S and the volume is 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 a specific number into a formula for evaluation, we should pay attention to the writing format: first write how many letters are equal, then write the original formula, and then substitute the number into the formula for evaluation. Letters represent numbers, and the unit name is not written after them.
In the same formula, the letters contained in the formula have different values, so the values of the formula are also different.
This paper is the knowledge point that we prepared for you to express numbers by letters in junior high school mathematics. I hope it will play a certain role in your study!