Unit 1 Decimal Multiplication
1, decimal multiplication integer (p2,3): meaning-a simple operation to find the sum of several identical addends.
For example, 1.5×3 indicates how many times 1.5 is or the sum of three 1.5.
Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; See how many decimal places a factor has, and count from the right of the product to the decimal point.
2. Decimal times decimal (P4, 5): that is, what is the score of this number.
For example, 1.5×0.8 is to find what is eight tenths of 1.5.
How much is 1.5× 1.8? It is 1.8 times 1.5.
Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; See how many decimal places a factor has, and count from the right of the product to the decimal point.
Note: In the calculation results, the 0 at the end of the decimal part should be removed to simplify the decimal; When the number of decimal places is not enough, use 0 to occupy the place.
3. Rule (1)(P9): the product of a number (except 0) multiplied by a number greater than 1 is greater than the original number;
A number (except 0) is multiplied by a number less than 1, and the product is less than the original number.
4. There are generally three methods to find the divisor: (P 10)
(1) rounding method; (2) into law; (3) Tailing method
5. Calculate the amount of money, with two decimal places reserved, which means that it is calculated to the minute, and one decimal place reserved, which means that it is calculated to the angle.
6. The operation of (p11) four decimal places is the same as that of an integer.
7, operation law and nature:
Addition: additive commutative law: a+b=b+a Addition Law: (a+b)+c=a+(b+c).
Subtraction: Subtraction property: A-B-C = A-(B+C) A-(B-C) = A-B+C.
Multiplication: multiplication commutative law: a× b = b× a.
Law of multiplicative association: (a×b)×c=a×(b×c)
Multiplication and distribution law: (a+b) × c = a× c+b× c (a-b) × c = a× c-b× c.
Division: nature of division: a÷b÷c=a÷(b×c)
Unit 2 Decimal Division
8. Significance of fractional division: Find the operation of another factor by knowing the product of two factors and one of them.
For example, 0.6÷0.3 means an operation to find another factor by knowing the product of two factors 0.6 and one factor 0.3.
9. Calculation method of decimal divided by integer (P 16): decimal divided by integer, divided by integer division. The decimal point of quotient should be aligned with the decimal point of dividend. If the integer part is not divided enough, point on the decimal point of quotient 0. If there is a remainder, add 0 and divide it.
10, (P2 1) Division calculation method with divisor as decimal: first expand the divisor and dividend by the same multiple to make the divisor an integer, and then calculate according to the rule of fractional division with divisor as integer.
Note: If there are not enough digits in the dividend, make it up with 0 at the end of the dividend.
1 1, (P23) In practical application, the quotient obtained by fractional division can also be rounded to a certain number of decimal places, thus obtaining the approximate number of quotients.
Division change of 12, (p24,25): ① quotient invariance: divisor and divisor expand or shrink by the same multiple at the same time (except 0), and the quotient remains unchanged; (2) the divisor remains the same, the dividend expands and the quotient expands; ③ The divisor is constant, the divisor is reduced, and the quotient is expanded.
13, (P28) Cyclic decimal: the decimal part of a number, starting from a certain bit, in which one or several numbers appear repeatedly. Such decimals are called cyclic decimals.
Cycle node: the decimal part of cycle decimal, which is a number that appears repeatedly in turn. For example, the loop node of 6.3232 ... is 32.
14. The number of digits in the decimal part is a finite decimal, which is called a finite decimal. The number of digits in the decimal part is infinite decimal, which is called infinite decimal.
Unit 3 Observing Objects
15, observing objects from different angles may lead to different shapes; When observing a cuboid or cube, you can see at most three faces from a fixed position.
Unit 4 Simple Equation
16, (P45) In a formula containing letters, the multiplication sign in the middle of the letters can be written as "?" , can also be omitted.
The plus sign, minus sign, division sign and multiplication sign between numbers cannot be omitted.
17, a×a can be written as a? A or a, a is pronounced as the square of a, and 2a stands for a+a.
18, equation: An equation with an unknown number is called an equation.
The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.
The process of solving an equation is called solving an equation.
19, principle of solving equation: balance.
The equation still holds when the left and right sides of the equation add, subtract, multiply and divide the same number (except 0) at the same time.
20, 10 quantitative relationship: addition: sum = addend+addend, one addend = and- two addends.
Subtraction: difference = minuend-meimei = difference+meimei = meimei-difference.
Multiplication: product = factor × factor One factor = product ÷ another factor.
Division: quotient = dividend/divisor = quotient × divisor = dividend/quotient
2 1. All equations are equations, but not all equations.
22. Equation test process: left side of equation = ...
23. The solution of the equation is a number;
The computational proces of solving an equation. = Right side of equation
So, X=… is the solution of the equation.
The area of the fifth unit polygon
23. Formula: rectangle: perimeter = (length+width) ×2- length = perimeter ÷2- width; Width = perimeter ÷2- Long letter formula: C=(a+b)×2
Area = length × width Letter formula: S=ab
Square: perimeter = side length ×4 letters formula: C=4a
Area = side length × side length letter formula: S=a
Area of parallelogram = base × high letter formula: S=ah
Area of triangle = base × height ÷ 2-base = area × 2 height; Height = area ×2÷ bottom.
Alphabetic formula: S=ah÷2
Trapezoidal area = (upper bottom+lower bottom) × height ÷2 letter formula: S=(a+b)h÷2.
Upper bottom = area ×2÷ height-lower bottom, lower bottom = area ×2÷ height-upper bottom;
Height = area ×2 (upper bottom+lower bottom)
24. Derivation of parallelogram area formula: shear and translation.
25. Derivation of triangle area formula: rotation
Parallelogram can be changed into rectangle;
Two identical triangles can be combined into a parallelogram,
The length of a rectangle is equivalent to the base of a parallelogram;
The base of parallelogram is equivalent to the base of triangle;
The width of the rectangle is equivalent to the height of the parallelogram;
The height of parallelogram is equivalent to the height of triangle;
The area of a rectangle is equal to the area of a parallelogram,
The area of parallelogram is equal to twice the area of triangle,
Because rectangular area = length x width, parallelogram area = bottom x height.
Because parallelogram area = base × height, triangle area = base × height ÷2.
26. Derivation of trapezoidal area formula: rotation
27. The second derivation method of triangle and trapezoid. The teacher said that he read books by himself.
Two identical trapezoids can be combined into a parallelogram, as long as you know.
The base of parallelogram is equivalent to the sum of the upper and lower bases of trapezoid;
The height of parallelogram is equivalent to the height of trapezoid;
The area of that parallelogram is equal to twice that of the trapezoid,
Because parallelogram area = bottom × height, trapezoid area = (upper bottom+lower bottom) × height ÷2.
28. The parallelogram with equal base and equal height has the same area; Triangles with equal bases and equal heights have equal areas;
The area of a parallelogram with equal base and equal height is twice that of a triangle.
29. The rectangular frame is drawn as a parallelogram with a constant perimeter and a smaller area.
30. Combination diagram: Convert it into a simple diagram and calculate it through addition and subtraction.
Unit 6 Statistics and Possibility
3 1, average = total quantity/total number of copies
32. The advantage of the median is that it is not affected by the data size, and it is more suitable to represent the approximate level of all data.
Unit 7 Mathematics Wide Angle
Numbers can be used not only to represent quantity and order, but also to encode.
34. Postal code: It consists of 6 digits, with the first 2 digits representing the province (city, autonomous region).
0 5 4 0 0 1
The first three digits indicate the postal area.
The first four digits represent counties (cities).
The last two digits represent the delivery office.
35. ID number: 18 digits.
1 3 0 5 2 1 1 9 7 8 0 3 0 1 0 0 1 9
Check code of birth date sequence code in Xingtai County, Xingtai City, Hebei Province
The penultimate number is used to indicate gender, the singular number means male, and the even number means female.