Summary of mathematical formulas for fourth grade primary school "Morning Bull's Nose" learning method
The four arithmetic operations
1, addition, subtraction, multiplication and division are collectively referred to as the four arithmetic operations.
2. In a calculation without parentheses, if there are only additions and subtractions or only multiplications and divisions, they must be calculated in order from left to right.
3. In calculations without parentheses, there are multiplication, division, addition, and subtraction. Multiplication and division must be calculated first, and then addition and subtraction.
4. If there are parentheses in the calculation, you must first calculate the inside of the parentheses, and then calculate the outside of the parentheses; the calculation order of the calculations inside the parentheses follows the above calculation order.
5, addition, subtraction, multiplication and division are collectively called the four arithmetic operations.
Regarding the operation of "0"
1, "0" cannot be used as a divisor; Letter representation: a÷0 error
2. Adding 0 to a number returns the original number; Letter representation: a＋0= a
3. Subtracting 0 from a number returns the original number Number; Letter representation: a-0= a
4, the minuend is equal to the minuend, the difference is 0; Letter representation: a-a = 0
5, a number multiplied by 0, still gets 0; Letter representation: a×0= 0
6 , 0 divided by any non-0 number, you get 0; letter representation: 0÷a (a≠0) = 0
7. 0÷0 cannot get a fixed quotient; 5÷0 cannot get a quotient.
position and direction
1. Determine or draw the specific location of an object based on direction and distance. ( scale , angle drawing and measurement)
Note: 1. Scale 2. North direction 3. Angle drawing
2. Relativity between positions. Will describe the mutual positional relationship between two objects. (Determination of observation points)
3, drawing of a simple road map.
4. The three elements of a map: legend, direction, and scale.
5． When determining the direction: A. First determine the observation point
(1) Starting from there, that is the observation point.
(2) The one after the word "在" is the observation point.
B stood at the observation point to look at the direction.
For example: ① 25° east by south (the angle marked 25° is close to the east)
② 35° west by north (the angle marked 35° is close to the west)
6. When describing a route and drawing a road map: there is only one line, and the lines are connected end to end.
7． The eight commonly used directions are: east, south, west, north, southeast, northeast, southwest, and northwest.
Laws of operation and simple operations:
1. Laws of addition:
1. Commutative law of addition: When two numbers are added, the positions of the addends are exchanged, and the sum remains unchanged. a b=b a
2. The associative law of addition: to add three numbers, you can add the first two numbers first, and then add the third number; or you can add the last two numbers first, and then add the first number. , and remain unchanged. (a + b + c = a + (b + c) These two laws of addition are often used together. For example: 165 + 93 + 35 = 93 + (165 + 35) What is the basis?
3, continuous subtraction Properties: Subtracting two numbers from a number is equal to the sum of the two numbers minus a-b-c=a-(b +c)
2. The law of multiplication:
1. The commutative law of multiplication: multiplying two numbers. , exchange the positions of the factors, and the product remains unchanged. a×b=b×a
2. The associative law of multiplication: to multiply three numbers, you can multiply the first two numbers first, and then multiply the third number, or you can first multiply them. Multiply the last two numbers and then multiply them by the first number, and the product remains unchanged. (a×b)×c = a×(b×c)
These two laws of multiplication are often used together. For example: 125. Simplified calculation of ×78×8
3. Distributive law of multiplication: The sum of two numbers is multiplied by one number. You can first multiply the two numbers by the two numbers, and then add the products.(a + b) × c = a × c + b × c (a - b) × c = a × c - b × c
Application of the multiplication distributive law:
① Type 1: (a + b) × c (a - b) ×c
= a× c + b×c = a× c - b×c
② Type 2: a × c + b × c a × c – b × c
= (a + b) × c = (a - b) × c
③ Type three: a × 99 + a a × b - a
= a × (99 + 1) = a × (b - 1)
④ Type four: a × 99 a × 102
= a × (100 - 1) = a × (100 + 2)
= a × 100 – a × 1 = a × 100 + a × 2
3. Simple calculation of
1. Simple calculation of continuous addition: ① Use the associative law of addition (combine those whose sum is a whole ten, a whole hundred, or a whole thousand)
② Units place: 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 Combined with 5.
③ Tens digit: 0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5, combined.
2． Simple calculation of continuous subtraction:
① Subtracting several numbers in a row is equal to subtracting the sum of these numbers. For example: 106-26-74=106-(26 +74)
② Subtracting the sum of several numbers is equivalent to subtracting these numbers continuously. For example: 106-(26 +74)=106-26-74
3. Simple calculation of mixed addition and subtraction:
The position of the first number remains unchanged, and the remaining addends and subtractions can exchange positions (you can add first or subtract first)
For example: 123 +38-23=123-23 + 38 146-78 +54=146 +54-78
4． Simple calculation of continuous multiplication:
uses the associative law of multiplication: combine common numbers together: 25 and 4; 125 and 8; 125 and 80. When
sees 25, he will look for 4, and when he sees 125, he will look for 8;
5. Simple calculation of continuous division:
①Dividing several numbers continuously is equal to dividing by the product of these numbers.
②Dividing the product of several numbers is equal to dividing these numbers continuously.
6. Simple calculation of mixed multiplication and division:
The position of the first number remains unchanged, and the remaining factors and divisors can exchange positions. (You can multiply or divide first)
For example: 27×13÷9=27÷9×13
4. Properties of continuous division: A number divided by two numbers continuously is equal to dividing by the product of the two numbers. a÷b÷c = a÷(b×c)
triangle
1. Definition of triangle: A figure surrounded by three line segments (the endpoints of each two adjacent line segments are connected or coincident) is called a triangle.
2. Draw a vertical line from a vertex of a triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle. This opposite side is called the base of the triangle. The triangle has only 3 heights. Focus: How to draw the height of a triangle.
3. Characteristics of triangles: 1. Physical characteristics: stability. Such as: bicycle tripod, tripod on telephone pole.
4. Characteristics of sides: The sum of any two sides is greater than the third side.
5. For the convenience of expression, the letters A, B, and C are used to represent the three vertices of the triangle respectively. The triangle can be expressed as triangle ABC.
6. Classification of triangles:
is divided according to the size of the angles: acute triangle, right triangle , obtuse triangle.
is divided according to the length of the sides: △ with three unequal sides, and isosceles △ (an equilateral triangle or an equilateral triangle is a special isosceles △).
The three sides of an equilateral △ are equal and each angle is 60 degrees. (The concepts of vertex angle, base angle, waist and base)
7. A triangle with three acute angles is called an acute triangle.
8. A triangle with one right angle is called a right triangle.
9. A triangle with one obtuse angle is called an obtuse triangle.
10. Every triangle has at least two acute angles; every triangle has at most 1 right angle; every triangle has at most 1 obtuse angle.
11. A triangle with two equal sides is called an isosceles triangle.
12. A triangle with three equal sides is called an equilateral triangle, also called an equilateral triangle.
13. An equilateral triangle is a special isosceles triangle.
14. The sum of the interior angles of a triangle is equal to 180 degrees. The sum of the interior angles of a quadrilateral is 360°. Calculation and format of related degrees.
15. Combination of graphics: Two identical triangles can definitely be combined into an parallelogram .
16. Two identical triangles can be used to form a parallelogram.
17. Use two identical right triangles to form a parallelogram, a rectangle, and a large triangle.
18. Use two identical isosceles right triangles to form a parallelogram or a square. A large isosceles right triangle.
19, dense tiling : Graphics that can be densely paved include rectangles, squares, triangles, regular hexagons, etc.
Addition and subtraction of decimals
1. Calculation rules: Align the same digits (align decimal points) and calculate according to the integer calculation method. The decimal point of the number should be aligned with the decimal point of the decimal on the horizontal line. The result is that decimals must be simplified based on the properties of decimals.
2, vertical calculation and verification. Note that the answer must be written on the horizontal form, not the result of the calculation.
3, the order of four arithmetic operations and the laws of operation of integers are also applicable to decimals. (Simplified calculation)
statistics:
1. Advantages of bar charts: intuitively reflect the quantity. Advantages of
2 and line statistical charts : they can reflect not only the quantity, but also the increase or decrease in quantity.
3. In the line statistical chart, the change trend refers to: rising or falling.
4. Line statistical chart: It uses one unit length to represent a certain quantity, traces each point according to the quantity, and then connects each point sequentially with line segments.
5. Advantages: Not only can you see the quantity, but you can also see the increase or decrease in quantity, predict future trends, and provide guidance and help for future production and life.
Mathematics wide angle: tree planting problem
(1) Tree planting problem:
1. Planting at both ends: number of intervals = total length ÷ spacing; total length = spacing × number of spacings; number of trees = number of spacings + 1; number of spacings = number of trees - 1
2, two No planting at the ends: number of intervals = total length ÷ spacing; total length = spacing : Number of trees = number of intervals + 1
2. Plant at one end, not plant at the other end: Number of trees = number of intervals
3. Don’t plant at both ends: number of trees = number of intervals - 1
4. Closed: number of trees = number of intervals
(2) Sawing problem : Number of segments = number of times + 1; number of times = number of segments - 1
Total time = each time × number of times
(3) Square matrix problem: The number of the outermost layer is: side length × 4-4 or (side length - 1) × 4
The total number of the entire square matrix is: side length × side length
(4) Closed graphics (such as a circle or oval): total length ÷ spacing = number of intervals; number of trees = number of intervals
(5) chessboard pieces Number:
1. The number of chess pieces on the outermost layer of the chessboard: the number of chess pieces on each side × the number of sides - the number of sides
2. The total number of chess pieces on the chessboard: the number of chess pieces in each row × the number of chess pieces in each column
3. The number of people in the outermost layer of the square array: the number of people on each side × 4-4
4. Flower pots placed on a polygon: number of flower pots placed on each side × number of sides - number of sides
