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; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.
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; Look at the number of decimal places in factor one * * *, and count the decimal points from the right side of the product.
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, and keep two decimal places, indicating that the calculation has reached the point. Keep one decimal place, indicating that the angle has been calculated.
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: Know the product of two factors and one of them, and find the operation of the other factor.
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 and then divided by integer. The decimal point of quotient should be aligned with the decimal point of dividend. The integer part is not divided enough, quotient 0, decimal point. If there is a remainder, add 0 and divide it.
10, (P2 1) Calculation method of division with divisor as decimal: first expand the divisor and dividend by the same multiple, so that the divisor becomes 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 up the dividend with 0 at the end.
1 1, (P23) In practical application, the quotient obtained by fractional division can also be "rounded" as needed.
Division change of 12, (p24,25): ① Quotient invariance: divisor and divisor expand or shrink by the same multiple (except 0) at the same time, and the quotient remains unchanged. (2) The divisor remains the same, the dividend expands, and the quotient expands. The dividend is constant, the divisor decreases and the quotient expands. ③ The dividend is constant, the divisor decreases and the quotient expands.
13, (P28) Cyclic decimal: the decimal part of a number. Starting from a certain number, one number or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals.
Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn. For example, the periodic part ......................... 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 the formula containing letters, the multiplication sign in the middle of the letters can be recorded as ""or omitted.
The plus sign, minus sign, division sign and multiplication sign between numbers cannot be omitted.
17, a×a can be written as 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. Quantitative relationship: addition: sum = addend+addend; One addend = sum-another addend.
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;
Calculation process of solving equations. = Right side of the equation
So, X=… is the solution of the equation.
The area of the fifth unit polygon
23. Formula:
Rectangular: perimeter = (length+width) ×2- length = perimeter ÷2- width; Width = perimeter ÷ 2- Long letter formula: C=(a+b)×2
Area = area = length × width Letter formula: S=ab
Square: perimeter = side length ×4 letters formula: C=4a
Area of parallelogram = base × high letter formula: S=ah
Area of triangle = base × height ÷2- base = area × 2 height; Height = area ×2÷ bottom letter 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 = because parallelogram area = base x height, triangle area = base x 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 that has been learned 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
33. Numbers can be used not only for quantity and order, but also for coding.
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.