Summary of knowledge points
1. location: the place where it is located or occupied.
2. Direction: refers to the east, west, south, north and other directions.
3. Division: The operation of finding another factor by knowing the product of two factors and one of them is called division.
If ab=c(b≠0), the operation of finding another factor A by multiplying the product C and the factor B is division, written as c/b, and read as C divided by B (or B divided by C). Among them, c is called dividend, b is called divisor, and the result of a operation is called quotient.
4. Division rule: How many digits is the divisor? Look at the first few digits of the divisor first. If the first few digits are not divided enough, look at another one. The quotient is written except one, which is not enough to quotient one and zero. The remainder is less than the divisor. If the quotient is decimal, the decimal point of the quotient should be aligned with that of the dividend. If the divisor is a decimal, it must be divided into integers and then calculated.
5. Quotient invariance: The divisor and divisor are multiplied or divided by a non-zero natural number at the same time, and the quotient remains unchanged.
6. The essence of division: a number divided by several numbers equals the product of this number divided by those numbers, which is the essence of division. Sometimes simple operations can be performed according to the nature of the division. Such as: 300÷25÷4=300÷(25×4).
7. The relationship between dividend, divisor and quotient:
Dividend is enlarged (reduced) by n times, and quotient is correspondingly enlarged (reduced) by n times.
The divisor is expanded (reduced) by n times, and the quotient is correspondingly reduced (expanded) by n times.
8. Pen division: First, according to the law of integer division, the decimal point of quotient should be aligned with the decimal point of dividend; If there is a remainder at the end of the dividend, add "0" after the remainder to continue the division.
9. Division calculation rules with divisor as decimal: first move the decimal point of divisor to make it an integer, then move the decimal point of divisor to the right by a few digits (add "0" if there are not enough digits), and then calculate according to the division rules with divisor as integer.
10. Mixed operation without brackets:
Operations at the same level are operated from left to right in turn; Two-stage operation calculates multiplication and division first, and then addition and subtraction.
1 1. First-level operation: addition and subtraction are called first-level operations.
12. Secondary operations: multiplication and division are called secondary operations.
13. Data: Data, also known as observed values, is the result of experiments, measurements, observations and investigations. , and often given in quantitative form.
14. data analysis: data analysis is a process in which an organization collects and analyzes data purposefully and makes it into information.
15. Steps and application of data analysis:
Data analysis is widely used. Typical data analysis may include the following three steps:
(1) Exploratory data analysis. When the data is first obtained, it may be chaotic and irregular. By means of drawing, tabulating, fitting various equations and calculating some characteristic quantities, the possible forms of regularity are explored, that is, from what direction and how to discover and reveal the regularity implied in the data.
(2) Model selection analysis, which puts forward one or several possible models on the basis of exploratory analysis, and then selects a certain model from them through further analysis.
(3) Inference analysis, usually using mathematical statistics to infer the reliability and accuracy of a given model or estimate.
16. Average
The average value refers to the sum of all data in a set of data divided by the number of data. The average value is a quantity representing the trend of a set of data sets and an index reflecting the trend of data sets.
The key to solve the problem of average application is to determine the "total amount" and the total number of copies corresponding to the total amount.
In statistical work, mean and standard deviation are the two most important measures to describe the trend and deviation of data sets.
17. 24-hour timing method
(1) Time division method (12 point method): A day starts at midnight 12, and the 24 hours of 1 day are divided into two sections, each of which is 12 hours. From 12 midnight to 12 noon is called the morning, and from 12 noon to 12 midnight is called the afternoon. This timing method is often used in life.
(2) 24-hour timing method: This is the 0-24-hour timing method adopted by radio stations, stations, post offices and other departments. According to this timing method, 1 pm is 13: 00, 2 pm is 14: 00... 12 pm is 24: 00.
18. Number names in the multiplication formula
"×" is a multiplication sign, the numbers before and after the multiplication sign are called factors, "=" is an equal sign, and the numbers after the equal sign are called products.
10 (factor) × (symbol) 200 (factor) = (symbol) 2000 (product)
19. Multiplication algorithm
Integer multiplication meets the following requirements: exchange law, association law, distribution law and elimination law.
With the development of mathematics, the object of operation has developed from integer to more general group.
Intra-group multiplication is no longer needed to satisfy the commutative law. The most famous noncommutative example is the quaternion group discovered by Hamilton. But the law of association is still satisfied.
(1) Multiplication commutation law: a× b = b× a.
(2) multiplicative associative law: (a×b)×c=a×(b×c)
(3) Multiplicative distribution law: (a+b) × c = a× c+b× c.
20. multiplication table
2 1. area: the size of the surface shape of objects is called their area.
22. The common units of area are square centimeter, square decimeter and square meter.
(1) A square with a side length of 1 cm and an area of1cm 2.
(2) A square with a side length of 1 decimeter and an area of 1 square decimeter.
(3) A square with a side length of 1m and an area of 1m2.
23. Large areas are generally measured in hectares and square kilometers.
(1) Square with side length 1 00m and area1hectare.
(2) Square with side length 1km and area 1km2.
24. Area calculation method
Rectangular: S=ab{ rectangular area = length × width}
Square: S=a2{ square area = side length × side length}
Parallelogram: S=ab{ parallelogram area = base × height}
Triangle: S=ab÷2{ triangle area = base × height ÷2}
Trapezoid: S=(a+b)×h÷2{ Trapezoid area = (upper bottom+lower bottom) × height ÷2}
Circle (perfect circle): S=πr2{ area of circle (perfect circle) = pi × radius}
25. Area measurement unit and ratio:
1 square kilometer = 100 hectare 1 square kilometer =10 million square meters.
1 ha = 1 0000m21m2 = 100 square decimeter (dm2)
1 square decimeter = 100 square centimeter (cm2).
26. hectare: the unit symbol of hectare is "hm2", where H stands for 1 00m, and hm2 stands for the square of100m, i.e.10000m2, i.e.1hectare.
27. Decimal: Decimal consists of integer part, decimal part and decimal point. When measuring an object, it is often not an integer, so the ancients invented decimals to supplement integer decimals, which is a special form of fractional fractions. Fractions with denominators of 10, 100, 1000 ... can be expressed in decimals. All fractions can be expressed as decimals, except infinite acyclic decimals, all decimals can express the number of components.
28. Basic properties of decimals: Add or remove 0 at the end of decimals, the size of decimals remains unchanged, but the counting unit has changed. Moreover, if the decimal point is moved one, two or three places to the left, the original number will be reduced by 10 times, 100 times and 1000 times; if the decimal point is moved one, two or three places to the right, the original number will be expanded by 10 times and 100 times.
29. Decimal writing: the integer part is written before the decimal point, the decimal part is written after the decimal point, and the middle is separated by the decimal point.
30. Decimal reading:
(1) Read by fraction. Read with integers with decimals. The fractional part is read by the fraction.
For example, 0.38 is pronounced as 38%, and 14.56 is pronounced as 14 and 56%.
(2) The integer part is still read as an integer, the decimal point is read as a "dot", and the decimal part reads the numbers on each digit in sequence. If there are several zeros repeated, you should not read only one zero.
For example: 0.45 is read as 0.45; 56.032 is read as 56.032; 1.0005 is pronounced one point zero five.