All concepts in primary school mathematics textbooks

First correct 1. It's not what it says. Every version is different, and what you have learned is different. For example, people's education edition learned less, but learned well, while Soviet education edition learned more, but did not learn well. I am in the sixth grade. The teacher sorted out some concepts for us and sent them to my mailbox for you to copy:

I. Integers and decimals

1. The smallest number is 1 and the smallest natural number is 0.

2. Meaning of decimals: Divide the integer "1" into 10, 100, 1000 ... These fractions are one tenth, percentage and one thousandth respectively ... which can be expressed by decimals.

3. The decimal point has an integer part on the left and a decimal part on the right, followed by decimal, percentile and thousandth. ...

4. Classification of decimals: Decimals are limited.

Infinite decimal infinite cyclic decimal

Infinite non-repeating decimal

Integers and decimals are numbers written in decimal notation.

6. Properties of decimals: Add 0 or remove 0 at the end of decimals, and the size of decimals remains unchanged.

7. Move the decimal point to the right by one, two and three places ... The original number is enlarged by 10 times, 100 times and 1000 times respectively. ...

The decimal point is shifted to the left by one place, two places and three places ... The original number is reduced by 10 times, 100 times and 1000 times respectively. ...

I. Divisibility of numbers

1. divisible: the integer A is divisible by the integer B (b≠0), and the divisible quotient is exactly an integer with no remainder, so we say that A can be divisible by B, or that B can be divisible by A. ..

2. divisor and multiple: If the number A is divisible by the number B, then A is called a multiple of B and B is called a divisor of A. ..

3. The number of multiples of a number is infinite, the minimum multiple is itself, and there is no maximum multiple.

The divisor of a number is finite, the smallest divisor is 1, and the largest divisor is itself.

4. According to whether it can be divisible by 2, natural numbers that are not 0 are divided into even numbers and odd numbers. Numbers that are divisible by 2 are called even numbers, and numbers that are not divisible by 2 are called odd numbers.

5. According to the divisor of a number, non-zero natural numbers can be divided into three categories: 1, prime number and composite number.

Prime number: If a number has only 1 and two divisors of itself, it is called a prime number. Every prime number has two divisors.

Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. A composite number has at least three divisors.

The smallest prime number is 2 and the smallest composite number is 4.

The prime numbers in 1~20 are: 2,3,5,7,1,13, 17, 19.

The complex number of 1~20 is "4,6,8,9, 10, 12, 14, 15, 16, 18".

6. Features of numbers divisible by 2: Numbers with digits of 0, 2, 4, 6 and 8 can be divisible by 2.

Features of numbers divisible by 5: Numbers with 0 or 5 bits can be divisible by 5.

The characteristics of numbers divisible by 3: the sum of the numbers in each bit of a number can be divisible by 3, and this number can also be divisible by 3.

7. Prime factor: If the factor of a natural number is a prime number, this factor is called the prime factor of this natural number.

8. prime factor decomposition: a composite number multiplied by a prime factor is called prime factor decomposition.

9. Common divisor, common multiple: the common divisor of several numbers is called the common divisor of these numbers; The largest one is called the greatest common divisor of these numbers.

The common multiple of several numbers is called the common multiple of these numbers; The smallest one is called the least common multiple of these numbers.

10. Find the greatest common divisor and the least common multiple of two numbers in a general relationship by short division; The greatest common divisor of two numbers of coprime relation is 1, and the least common multiple is the product of two numbers; In the multiple relation, the greatest common divisor of two numbers is decimal, and the smallest common multiple is large.

1 1. Prime number: Two numbers whose common divisor is only 1 are called prime numbers.

12. The product of two numbers is equal to the product of the least common multiple and the greatest common divisor.

Three. Four operations

1. One addend = and-the other addend is minuend = difference+meiosis = minuend-difference.

One factor = product/dividend of another factor = quotient × divisor = dividend/quotient

2. Among the four operations, addition and subtraction are called primary operations, and multiplication and division are called secondary operations.

3. Operating rules:

(1) additive commutative law: a+b=b+a multiplicative commutative law: a× b = b× a.

When two numbers are added, the positions of addends are exchanged, and their sum remains the same.

When two numbers are added, the position of the exchange factor remains unchanged.

(2) additive associative law: (a+b)+c=a+(b+c) multiplicative associative law: (a×b)×c=a×(b×c)

Add three numbers, first add the first two numbers and then the third number; Or add the last two numbers first, and then add them to the first number, and their sum remains the same.

Multiplication of three numbers: first multiply the first two numbers and then multiply the third number; Or multiply the last two numbers first, and then multiply them with the first number, and their products remain unchanged.

(3) Multiplicative distribution law: (a+b) × c = a× c+b× c.

Multiply the same number by the sum of two numbers, you can multiply the two addends by this number respectively, and then add the two products, and the result remains the same.

(4) nature of subtraction: a-b-c=a-(b+c) nature of division: a \b \c = a \b×c c.

Subtracting two numbers in a row from a number is equivalent to subtracting the sum of two subtractions from this number.

A number divided by two consecutive numbers is equal to the product of this number divided by two divisors.

Four. relationship

1. Speed× time = distance ÷ time = speed ÷ distance ÷ speed = time.

Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.

Unit price × quantity = total price ÷ total price ÷ quantity = unit price ÷ total price ÷ unit price = quantity

Verb (abbreviation for verb) equation

1. Equation: An equation with an unknown number is called an equation.

2. Solution of the equation: The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.

3. Solving equations: The process of solving equations is called solving equations.

Fractions and percentages of intransitive verbs

The meaning of 1. Score: divide the unit "1" into several parts on average, and the number representing such one or several parts is called a score.

2. Decimal unit: the unit "1" is divided into several parts on average, and the number representing one part is called decimal unit.

3. The connection between fraction and division: the numerator of fraction is the dividend in division, and the denominator is the divisor in division.

Relationship between fractions and decimals: decimals are actually fractions with denominators of 10, 100, 1000.

The connection between the fraction and the ratio: the numerator of the fraction is the former term of the ratio, and the denominator of the fraction is the latter term of the ratio.

4. Classification of scores: scores can be divided into true scores and false scores.

5. True fraction: The fraction with numerator less than denominator is called true fraction. The true score is less than 1.

False fraction: Fractions with numerator greater than or equal to denominator are called false fractions. False score is greater than or equal to 1.

Simplest fraction: The reciprocal fraction of numerator and denominator is called simplest fraction.

7. The basic nature of the score: the numerator and denominator of the score are multiplied or divided by the same number at the same time (except zero), and the size of the score remains unchanged.

8. Such a fraction can be converted into a finite decimal: assuming that the fraction is the simplest fraction, if the denominator only contains two prime factors, 2 and 5, such a fraction can be converted into a finite decimal.

9. Percentage: The number that indicates that one number is the percentage of another number is called percentage. Percentages are also called percentages or percentages. Percentages are usually expressed as "%".

Seven. Quantitative measurement

1. Length units are: kilometers, meters, decimeters, centimeters and millimeters. Write down the forward speed between them.

The units of area are: square kilometers, hectares, square meters, square decimeters and square centimeters. Note the progress between them.

Volume units are: cubic meter, cubic decimeter (liter) and cubic centimeter (milliliter). Write down the forward speed between them.

The units of mass are tons, kilograms and grams. Note the progress between them.

Time units are: century, year, month, day, hour, minute and second. Write down the progress between them.

2. The big months of the year are: 1, 3, 5, 7, 8,/kloc-0, 65438+February, ***7, and 3 1 day per month.

There are: April, June, September, 165438+ 10, ***4, 30 days per month.

February in a normal year has 28 days and leap year has 29 days.

The method of recording the moon with left fist

There are four quarters in a year and three months in each quarter.

4. Leap year in normal years: a leap year is usually a multiple of 4 in the Gregorian calendar year, which is a whole hundred, and it must be a multiple of 400 to be considered a leap year.

5. Nominal number: the measured number and the unit name are collectively called nominal number.

Single number: a single number with only one company name is called a single number.

Composite number: A compound number is one with two or more unit names.

6. Name rewriting: the multiplication rate of the high-grade unit name converted into the low-grade unit name, and the low-grade unit name converted into the high-grade unit name divided by the multiplication rate.

Eight. Basic knowledge of geometry

1. The connection and difference between line segment, ray and straight line: the connection is that all three are straight lines, but the difference is that the line segment has two endpoints and its length can be measured; Ray has only one endpoint and can extend indefinitely; A straight line has no end points, and both ends can extend indefinitely. Rays and straight lines are infinitely long.

2. Angle: A figure composed of two rays drawn from a point is called an angle.

3. The size of the angle: The size of the angle depends on the size of both sides. The bigger the fork, the bigger the angle.

4. The unit of measuring angle: degree, which is indicated by the symbol "0".

5. An angle less than 90 is called an acute angle; An angle greater than 90 and less than180 is called an obtuse angle. The angle between two sides in a straight line is called a right angle. Boxer 180.

6. Vertical line: When two straight lines intersect at right angles, they are perpendicular to each other, one of which is the vertical line of the other, and the intersection of these two straight lines is called vertical foot. (Description of drawings)

7. Parallel lines: Two straight lines that do not intersect on the same plane are called parallel lines. It can also be said that these two straight lines are parallel to each other.

The vertical segments between parallel lines are all equal in length.

8. Triangle: A figure surrounded by three line segments is called a triangle.

9. The classification of triangle:

(1) By angle: acute triangle, obtuse triangle, right triangle.

(2) Divided by sides: general triangle, isosceles triangle and equilateral triangle.

10. The sum of the three internal angles of a triangle is 180.

Quadrilateral: a figure surrounded by four line segments.

12. The circle is a curve figure. The distance from any point on the circle to the center of the circle is equal, and this distance is the length of the radius of the circle.

13. There are countless circles in radius and diameter. The diameter of the same circle is twice the radius, and the radius is half the diameter.

14. Axisymmetric graph: If a graph is folded in half along a straight line, two graphs of the straight line can completely overlap, and this graph is an axisymmetric graph. The straight line where the crease lies is called the symmetry axis.

15. The axisymmetric figures in the learned figures are: circle, isosceles triangle, equilateral triangle, rectangle, square and isosceles trapezoid.

16. Perimeter: The sum of all the side lengths surrounding a graph is the circumference of the graph.

Area: The size of an object's surface or closed plane figure is called their area.

17。 Surface area: The sum of all the areas of a three-dimensional figure is called the surface area of this three-dimensional figure.

Volume: The size of the space occupied by an object is called the volume of the object.

18. Both cuboids and cubes have 12 sides, 6 faces and 8 vertices.

A cube is a special cuboid and an equilateral triangle is a special isosceles triangle.

19. Three characteristics of the cylinder: (1) The thickness of the top and bottom is the same; (2) The side is curved; (3) The two bottom surfaces are the same circle.

20. Height of cylinder: The distance between two bottom surfaces of cylinder is called the height of cylinder. A cylinder has countless heights, all of which are parallel and equal.

2 1. Expand the side of the cylinder to get a rectangle. The length of this rectangle is equal to the circumference of the bottom of the cylinder, and the width is equal to the height of the cylinder.

22.Pi π is an infinite acyclic decimal. π=3. 14 1592653……

23. Divide the circle into several parts, and the figure is close to a rectangle. The length of this rectangle is half of the circumference, and the width is the radius of the circle.

24. Height of the cone: The distance from the apex of the cone to the center of the bottom surface is the height of the cone.

25. The volume of a cone with equal bottom and equal height is cylindrical, and the volume of a cylinder with equal bottom and equal height is three times that of a cone.

For cylinders and cones with equal volume and bottom area, the height of the cylinder is conical and the height of the cone is three times that of the cylinder.

Nine. Ratio and proportion

Meaning of 1. ratio: The division of two numbers is also called the ratio of two numbers.

Meaning of proportion: Two expressions with equal proportions are called proportions.

2. Find the ratio: the quotient obtained by dividing the former term of the ratio by the latter term of the ratio is called the ratio.

3. The basic nature of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number (except 0), and the ratio remains unchanged.

The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.

4. The basic properties of application ratio can be simplified;

Using the basic properties of proportion, we can judge whether two proportions can form a proportion, and we can also find out the unknown term in the proportion, that is, the solution ratio.

5. Use letters to express the relationship between ratio and division and fraction.

a:b=a÷b= (b≠0)

6. Scale: We call the ratio of the distance on the map to the actual distance the scale of this map.

7. Distance on the map: actual distance = proportion

Or = scale

Actual distance = distance on the map/distance on the scale map = actual distance × scale.

8. Method of finding the ratio: According to the meaning of the ratio, divide the former item by the latter item, and the result is a number.

Method of simplifying the ratio: According to the basic properties of the ratio, multiply or divide the first and second items of the ratio by the same number (except zero), and the result is the simplest integer ratio.

9. Proportional relationship: two related quantities, one change and the other change. If the ratio (that is, quotient) of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship.

Use the formula: =k (certain), and graphically illustrate that the proportional relationship is a straight line.

10. Inverse relationship: two related quantities, one changes and the other changes. If the product of the corresponding two numbers in these two quantities is certain, then these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship.

Expressed by formula: x×y=k (definite), graphically expressed, and the inverse ratio relationship is a curve.

Simple statistics

1. Common statistical charts include bar chart, line chart and fan chart.

2. Features of bar graph: (1) A certain quantity is expressed by unit length. (2) Use the length of the straight bar to express the quantity. Function: From the figure, we can clearly see the figures of each quantity for comparison.

Features of broken-line statistical chart: (1) A certain quantity is expressed by unit length. (2) The fluctuation of broken lines indicates the increase or decrease of quantity. Function: you can clearly see the change of quantity and quantity from the picture.

Arrangement of eleven formulas

Plane graphics:

1. rectangle:

Circumference = (length+width) ×2 C Length =(a+b)×2

Area = length × width s Length =a ×b

2. Square:

Perimeter = side length ×4 C plus =a×4

Area = side length × side length s positive =a×a

3. The area of parallelogram = base × height s flat =ah.

4. Area of triangle = base × height ÷2 S =ah÷2.

5. Trapezoidal area = (upper bottom+lower bottom) × height ÷2 S step =(a+b)×h÷2.

6. The circumference of a circle = diameter ×3. 14 C circle = π d.