1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.

2. The law of addition and association: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged.

3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.

4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the last two numbers are multiplied first and then the third number, and their products are unchanged.

5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged. For example, (2+4) × 5 = 2× 5+4× 5.

6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged.

Divide by any number that is not.

Simple multiplication: multiplication of multiplicand and multiplier, ending with O. You can multiply 1 before o first, and zero does not participate in the operation, and add a few zeros at the end of the product.

7. What is an equation? An equation in which the value on the left of the equal sign is equal to the value on the right of the equal sign is called an equation.

Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number, the equation is still valid.

8. What is an equation? A: Equations with unknowns are called equations.

9. What is a linear equation with one variable? Answer: An equation with an unknown number of one degree is called a linear equation of one variable.

Learn the example method and calculation of linear equation of one variable, that is, substitute χ into the formula to calculate.

10, fraction: divide the unit "1" into several parts on average, and the number representing such a part or fraction is called a fraction.

1 1, addition and subtraction of fractions: add and subtract fractions with the same denominator, only add and subtract numerators, and the denominator remains unchanged. Add and subtract fractions with different denominators, divide first, then add and subtract.

12. Fraction comparison: Compared with the denominator, the numerator is large and the numerator is small. Compared with the denominator, the scores of different denominators are divided first and then compared; If the numerator is the same, the denominator is big and small.

13, the fraction is multiplied by the integer, and the numerator is the product of the numerator of the fraction multiplied by the integer, and the denominator remains unchanged.

14, the fraction times the fraction, the numerator is the product of the numerator multiplication, and the denominator is the product of the denominator multiplication.

15, the fraction divided by an integer (except 0) is equal to the fraction multiplied by the reciprocal of this integer.

16, true fraction: the fraction with numerator less than denominator is called true fraction.

17. False fraction: the fraction with numerator greater than denominator or numerator equal to denominator is called false fraction. False score is greater than or equal to 1.

18, with fraction: write false fraction as integer and true fraction, which is called with fraction.

19, the basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.

20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.

2 1, the number A divided by the number B (except 0) equals the reciprocal of the number A multiplied by the number B. 。

Law of fractional addition and subtraction: Fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator remains the same. Add and subtract fractions with different denominators, divide first, then add and subtract.

Multiplication of fractions: use the product of molecules as numerator and the product of denominator as denominator.

22. What is the ratio? The division of two numbers is called the ratio of two numbers. Such as 2÷5 or 3:6 or 1/3.

The first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

23. What is proportion? Two formulas with equal ratios are called ratios, such as 3: 6 = 9: 18.

24. The basic nature of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.

25. Solution ratio: Find the unknown term in the ratio, which is called solution ratio, such as 3: χ = 9: 18.

26. Proportion: two related quantities, one changes and the other changes. If the corresponding ratio (i.e. quotient k) of these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example, y/x=k( k must) or kx = y.

27. Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. For example, x x×y = k( k must) or k/x = y.

28. Percentage: The number that indicates that one number is the percentage of another number is called percentage. Percent is also called percentage or percentage.

29. To convert a decimal into a percentage, just move the decimal to the right by two places and add a hundred semicolons after it. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%.

To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.

3 1. Fractions are converted into percentages, generally converted into decimals first (except for those that are inexhaustible, three decimal places are generally reserved), and then converted into percentages. In fact, to convert a fraction into a percentage, you need to convert it into a decimal and then multiply it by 100%.

32, the percentage of the number of components, first rewrite the percentage of the number of components, can be turned into the simplest score.

33. Learn how to divide scores into fractions and how to divide fractions into decimals.

34. greatest common divisor: several numbers can be divisible by the same number at the same time, and this number is called the greatest common divisor of these numbers. (or the common divisor of several numbers is called the greatest common divisor of these numbers. The largest one is called the greatest common divisor. )

35. Prime number: The common divisor is only 1, which is called prime number.

36. Least common multiple: the common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.

37. Comprehensive score: changing scores of different denominators into scores of the same denominator is equal to the original score, which is called comprehensive score. (Generally, the lowest common multiple is used for scores)

38. Degrade: When a score is equal to it, but the numerator and denominator are relatively small, it is called degrade.

Simplest fraction: A fraction whose numerator and denominator are prime numbers is called the simplest fraction. At the end of the score calculation, the number must be converted into the simplest score.

4 1, numbers with 0, 2, 4, 6 and 8 in the unit can be divisible by 2, that is, can be binary.

42. A number with a bit of 0 or 5 can be divisible by 5, that is, it can be subtracted by 5. Pay attention to the use when restoring.

Even and odd numbers: Numbers divisible by 2 are called even numbers. Numbers divisible by 2 are called odd numbers.

44. Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).

45. Complex number: A number is called a complex number if it has other divisors besides 1 and itself. 1 is neither prime nor composite.

46. Interest = principal × interest rate × time (time is generally in years or months, which should correspond to the unit of interest rate).

47. Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal within one year is called annual interest rate. The ratio of interest to principal in January is called monthly interest rate.

48. Natural number: an integer used to represent the number of objects, called natural number. 0 is also a natural number.

49. Cyclic decimal: A decimal in which one or more numbers are repeated from a certain position in the decimal part. Such decimals are called cyclic decimals. Like 3. 14 14 14.

50. acyclic decimal: decimal. From the decimal part, no number or several numbers appear repeatedly. Such a decimal is called an acyclic decimal. For example, pi: 3. 14 1592654.

5 1, infinite circulating decimal: a decimal, from the decimal part to the infinite digits, without one or several numbers repeating in turn, is called infinite circulating decimal. For example, 3. 14 1592654 ...

52. What is algebra? Algebra is to replace numbers with letters.

53. What is algebraic expression? Expressions expressed in letters are called algebraic expressions. For example, 3x = ab+c.

The second part: the quantitative relationship of the first network in the new curriculum standard.

1, unit price × quantity = total price 2, single output × quantity = total output.

3, speed x time = distance 4, efficiency x time = total work.

5. Appendix+Appendix = and one addend = and+another addend

6. Negative-negative = differential negative = negative-differential negative = negative+difference

7. Factor × factor = product one factor = product ÷ another factor.

8. Divider Divider = quotient divisor = dividend = quotient dividend = quotient x divisor

9. Division with remainder: dividend = quotient × divisor+remainder

10, a number is continuously divided by two numbers. You can multiply the last two numbers first, and then divide this number by their product, and the result remains the same. Example: 90 ÷ 5 ÷ 6 = 90 ÷ (5× 6).

Part III: Inter-unit prepayment rate

1 km =1km1km =1000m1m =10 decimeter1decimeter =10cm/kloc-.

1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter

1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter 1 cubic centimeter = 1000 cubic millimeter.

1 ton = 1 000kg 1 kg = 1 000g =1kg = 2kg1hectare =10000m2.

1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.

Part IV: Geometry knowledge.

Area of triangle = base × height ÷2. Formula S= a×h÷2 square area = side length× side length formula s = a× a.

Area of rectangle = length× width formula S = a× area of parallelogram = bottom× height formula S= a×h

Area of trapezoid = (upper bottom+lower bottom) × height ÷2 Formula S=(a+b)h÷2 Sum of internal angles: Sum of internal angles of triangle = 180 degrees.

Volume of cuboid (or cube) = bottom area × height formula: V=abh.

Circumference = diameter × π formula: c = π d = 2π r

Area of circle = radius × radius× π formula: s = π R2.

Surface (side) area of cylinder: The surface (side) area of cylinder is equal to the perimeter of bottom multiplied by height. Formula: s = ch = π dh = 2π rh.

Surface area of a cylinder: the surface area of a cylinder is equal to the perimeter of the bottom multiplied by the height plus the area of the circles at both ends. Formula: S=ch+2s=ch+2πr2.

Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh

Volume of cone = 1/3 bottom× product height. Formula: V= 1/3Sh.

Parallel lines: Two straight lines that do not intersect the same plane are called parallel lines.

Perpendicular: Two straight lines intersect at right angles. For two straight lines like this, we say they are perpendicular to each other. A straight line is called the perpendicular of another straight line, and the intersection of these two straight lines is called vertical foot.

General operating rules

65438+ 0× number of shares per share = total number of shares = total number of shares = number of shares = number of shares.

2 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple

3 speed × time = distance distance ÷ speed = time distance ÷ time = speed

4 unit price × quantity = total price/total price = total quantity/quantity = unit price

5 working efficiency × working time = total work amount ÷ working efficiency = working time ÷ total work amount ÷ working time = working efficiency

6 addend+addend = and-one addend = another addend.

7 minuend-minuend = difference minuend-difference = minuend difference+minuend = minuend

8 factor × factor = product product ÷ one factor = another factor

9 Dividend Divider = quotient divisor = divisor quotient × divisor = dividend

Calculation formula of mathematical graphics in primary schools

1 square c perimeter s area a side length perimeter = side length× 4c = 4a area = side length× side length s = a× a.

2 cubic V: volume A: side length surface area = side length × side length× 6 s Table =a×a×6

Volume = side length × side length × side length v = a× a× a.

3 rectangle c perimeter s area a side length

Circumference = (length+width) ×2 C=2(a+b) Area = length × width S=ab

4 cuboid v: volume s: area a: length b: width h: height xkb 1.com

Surface area (length× width+length× height+width× height )× 2s = 2 (AB+AH+BH) Volume = length× width× height V=abh.

5 triangle s area a base h height

Area = base × height ÷2 s=ah÷2 triangle height = area× 2 triangle base = area× 2 triangle height.

6 parallelogram s area a bottom h height area = bottom x height s=ah

7 trapezoid s area a upper bottom b lower bottom h height area = (upper bottom+lower bottom) × height ÷2 s=(a+b)× h÷2.

8 circle s area c perimeter ∏ d= diameter r= radius perimeter = diameter x ∏ = 2 x ∏× radius c = ∏ d = 2 ∏ r.

Area = radius × radius ×∈

9 cylinder v: volume h: height s; Bottom area r: bottom radius c: bottom perimeter

Lateral area = perimeter of bottom surface × high surface area = lateral area+bottom area× 2 volume = bottom area× high volume = lateral area ÷2× radius.

10 cone v: volume h: height s; Bottom area r: bottom radius volume = bottom area × height ÷3