Unit 1 Decimal Multiplication
1, decimal times integer:
@ Meaning- A simple operation to find the sum of several identical addends.
For example, 1.5×3 represents a simple operation to find the sum of three 1.5 (or what is three times 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:
Meaning-is to find a fraction of this number.
For example, 1.5×0.8 is how much is eight tenths of 1.5 (or how much is 1.8 multiplied by 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.
Note: After calculating the product with integers, you should remove the 0 at the end of the decimal, that is, simplify the decimal; When the number of digits is not enough, use 0 to occupy the place.
3. Rule: Except 0) times greater than
The product of the number of 1 is greater than the original number;
Except 0) multiplied by a number less than 1, and the product is less than the original number.
4. There are usually three ways to find the approximate value:
(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 order and law of decimal four operations are the same as those of integers.
7, operation law and nature:
@ Add:
Additive commutative law: A+B = B+A.
Additive associative law: (a+b)+c=a+(b+c)
Subtraction:
@ Multiply:
Multiplicative 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:
b c = a(b×c)
a \(b×c)= a \b \c
Second unit position
1, number pair: consists of two numbers, separated by commas and enclosed by brackets. The numbers in brackets are the number of columns and the number of rows from left to right, that is, "columns first, then rows".
2. Function: A set of numbers set the position of a unique point. Longitude and latitude are the principles. Example: In the grid diagram (plane rectangular coordinate system), it is represented by several pairs (3, 5) (third column, fifth row). note:
(1) In a plane rectangular coordinate system, the coordinates on the X axis represent columns and the coordinates on the Y axis represent rows. For example, the number pair (3, 2) represents the third column and the second row.
(2) Logarithm (x, 5) remains unchanged, indicating a horizontal line, and the number of columns (5, y) remains unchanged, indicating a vertical line. (A number is uncertain and a point cannot be determined)
2. The number of lines translated left and right remains unchanged; The number of columns in the chart that move up and down remains the same.
Unit 3 Decimal Division
1, the meaning 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 that the product of two known factors is 0.6, and one factor is 0.3 to find the other factor.
2. Calculation method of decimal divided by integer: 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.
3. Division calculation method with divisor as decimal: first expand the divisor and dividend by the same multiple to make the divisor become 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.
4. In practical application, the quotient obtained by fractional division can also be rounded to a certain number of decimal places as needed to obtain the approximate number of quotients.
5, the law of division of labor changes:
(1) Quotient remains unchanged: the dividend and divisor are expanded or reduced 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.
③ The dividend is constant, the divisor decreases and the quotient expands.
6. 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 period of 6.3232 is 32.
7. 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 4 Possibility
1. Some events are certain and some are uncertain.
maybe
The possibility is uncertain.
2. The chance (or probability) of an event is large or small.
A large amount, a small amount, a small amount
Unit 5 Simple Equation
1. In formulas containing letters, the multiplication sign in the middle of the letters can be recorded as ""or omitted. Note: The plus sign, minus sign, division sign and multiplication sign between numbers cannot be omitted.
22.a×a can be written as a or read as the square of a.
2. Note: 2a stands for A+A; A stands for a× a.
3. Equation: An equation with an unknown number is called an equation.
4. The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.
5. The process of solving the equation is called solving the equation.
6. Principle of solving equations: 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.
7, 10 quantitative relationship:
@ addition;
Sum = addend+addend;
= sum- two addends
@ subtraction:
= minuend-minuend;
= difference+subtraction;
Subtraction = minuend-difference
@ Multiply:
Product = factor × factor;
One factor = product ÷ another factor
@ Division:
Quotient = divider-divider;
= quotient × divisor;
Divider = Divider
Unit 6 Area of Polygon
1, rectangle:
@ circumference = (length+width) ×2- length = circumference ÷2- width; Width = perimeter ÷2- length
Letter representation: C=(a+b)×2
@ Area = length× width
Letter: S=ab
2. Square:
@ perimeter = side length ×4
Letter: C=4a
@ Area = side length × side length
Two letters: s = a.
3. Area of parallelogram = base × height
Letter: S=ah
4. Area of triangle = base × height ÷2—— base = area × 2 height; Height = area ×2÷ bottom.
Letter: S=ah÷2
5. Trapezoidal area = (upper bottom+lower bottom) × height ÷2
The letter means: S=(a+b)h÷2= area ×2÷ height-bottom,
Bottom = area ×2÷ height-upper bottom;
= area ×2 (upper bottom+lower bottom)
6. Derivation of parallelogram area formula: shearing, translation and cutting.
7. Derivation of triangle area formula: rotating splicing method.
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.
8. Derivation of trapezoidal area formula: rotating splicing method.
9. Two identical trapezoids can be combined into a parallelogram;
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.
10, 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.
1 1. The rectangular frame is drawn as a parallelogram with the same perimeter and smaller area.
12, combined graphic area (or shadow area): Convert it into a simple graphic that has been learned and calculate it by addition and subtraction (whole-part = another part).