Part I: Concept.

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

2. 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 is unchanged.

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

4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the second two numbers are multiplied first, and then the third number is multiplied, and the product remains 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.

Such as: (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 0 by any number other than 0 to get 0.

Simple multiplication: Multiplied by 0 at the end of the multiplier. You can multiply 1 before 0, and 0 does not participate in the operation. Drop a few 0s at the end of the product before adding.

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 at the same time, the equation is still valid.

8. What is Equation A: An equation with an unknown number is an equation.

9. What is a linear equation with one variable? A: A linear equation with an unknown number and an unknown degree.

Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated.

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

1 1, addition and subtraction of fractions: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.

12, comparison of fractional size: Compared with the fraction of denominator, the numerator is large and the numerator is small.

Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small.

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

14, the fraction multiplied by the fraction, the product multiplied by the numerator is the numerator, and the product multiplied by the denominator is the denominator.

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, a divided by b (except 0) equals the reciprocal of a times 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. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.

The multiplication of fractions is: 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 proportions. For example, 3: 6 = 9: 18

24. Basic properties of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.

25. Solution ratio: Finding the unknown term in the ratio is called solution ratio. Such as 3: χ = 9: 18.

26. Proportion: two related quantities, one of which 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 be) or kx = y.

27. Inverse proportion: two related quantities, one quantity changes and the other quantity changes. 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×y = k( k must be) or k/x = y.

28. Percent: A number indicating that one number is the percentage of another number is called percentage. Percentages are also called percentages or percentages.

29. To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the back. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%.

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

3 1, the fraction is converted into a percentage. Usually, the fraction is converted into a decimal (except for the inexhaustible three decimal places), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction 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.

We should learn how to divide fractions into components and 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 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 a 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: Divide scores with different denominators into scores with the same denominator equal to the original score, which is called comprehensive score. (Common divisor is the least common multiple)

38. Reduced fraction: It is called reduced fraction to change a fraction into an equal fraction, but the numerator and denominator are smaller. (The greatest common divisor is used for divisor)

39. simplest fraction: A fraction whose numerator and denominator are prime numbers is called simplest fraction.

40. At the end of the score calculation, the score must be converted into the simplest score.

4 1, the number of 0, 2, 4, 6 and 8 in the unit can be divisible by 2, that is, it can be divisible by 2. 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 of contracts.

43. Even and odd numbers: Numbers divisible by 2 are called even numbers. Numbers that are not divisible by 2 are called odd numbers.

44. prime number: A number is called a prime number if it only has 1 and its two divisors.

45. Composite number: a number. If there are other divisors besides 1 and itself, such a number is called a composite number. 1 is neither prime nor composite.

46. Interest = principal × interest rate × time (time is usually 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 for 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, starting from a certain place in the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14

50. Acyclic decimal: a decimal, starting from the decimal part, without one number or several numbers repeating in turn. Such a decimal is called acyclic decimal. For example, pi: 3. 14 1592654

5 1, infinite acyclic decimal: a decimal, from the decimal part to the infinite digits, is called infinite acyclic decimal without one or several numbers appearing in turn repeatedly. Like 3. 14 1592654……

52. What is algebra? Algebra means replacing numbers with letters.

53. What is an algebraic expression? Expressions expressed in letters are called algebraic expressions. For example 3x = AB+C.

The Complete Works of Mathematical Formulas in Primary Schools, Part II: Calculation Formulas.

Quantitative relationship:

1, each copy × number of copies = total number of copies ÷ number of copies = total number of copies ÷ number of copies = number of copies.

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

3. Speed × time = distance/speed = time/distance/time = speed

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

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

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

7. Minus-Minus = Minus-Minus = Minus+Minus = Minus

8. Factor × factor = product ÷ One factor = another factor.

9. Dividend = quotient dividend = divisor quotient × divisor = dividend

Formula of sum and difference problem

(sum+difference) ÷2= large number (sum-difference) ÷2= decimal.

Summation formula and multiple problems

Sum ÷ (multiple-1) = decimal × multiple = large number (or sum-decimal = large number)

Difference problem

Difference ÷ (multiple-1)= decimal × multiple = large number (or decimal+difference = large number)

Tree planting problem:

1 The problem of planting trees on unclosed lines can be divided into the following three situations:

(1) If trees are planted at both ends of the non-closed line, then:

Plant number = number of nodes+1= total length ÷ plant spacing-1 total length = plant spacing × (plant number-1) plant spacing = total length ÷ (plant number-1)

2 If you want to plant trees at one end of the unclosed line and not at the other end, then:

Number of plants = number of segments = total length/plant spacing = plant spacing × plant number = total length/plant number

(3) If no trees are planted at both ends of the non-closed line, then:

Number of plants = number of nodes-1= total length ÷ plant spacing-1 total length = plant spacing × (number of plants+1) plant spacing = total length ÷ (number of plants+1)

The quantitative relationship of planting trees on the closed line is as follows

Number of plants = number of segments = total length/plant spacing = plant spacing × plant number = total length/plant number

The question of profit and loss

(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.

(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.

(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.

encounter a problem

Meeting distance = speed × meeting time

Meeting time = meeting distance/speed and

Speed Sum = Meeting Distance/Meeting Time

Catch up with the problem

Catch-up distance = speed difference× catch-up time

Catch-up time = catch-up distance ÷ speed difference

Speed difference = catching distance ÷ catching time

Tap water problem

Downstream velocity = still water velocity+current velocity

Countercurrent velocity = still water velocity-current velocity

Still water velocity = (downstream velocity+countercurrent velocity) ÷2

Water velocity = (downstream velocity-countercurrent velocity) ÷2

Centralized question:

Solute weight+solvent weight = solution weight.

The weight of solute/solution × 100%= concentration.

Solution weight × concentration = solute weight

Solute weight-concentration = solution weight.

Profit and discount issues:

Profit = selling price-cost

Profit rate = profit/cost × 100%= (selling price/cost-1)× 100%.

Up and down amount = principal × up and down percentage

Discount = actual selling price ÷ original selling price× 1 00% (discount <1)

Interest = principal × interest rate× time

After-tax interest = principal × interest rate × time ×( 1-20%)

Area and volume conversion

(1)1km =1km =1000m1m =10 decimeter1decimeter =10 cm/kloc.

(2) 1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter.

(3) 1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter 1 cubic centimeter = 1000 cubic millimeter.

(4) 1 hectare = 1 ten thousand square meters 1 mu =666. 666 square meters

(5) 1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.

Weight conversion:

1t = 1000kg 1kg = 1000g 1kg = 1kg。

Rmb unit conversion

1 yuan = 10 angle 1 angle = 10 point 1 yuan = 100 point.

Time unit conversion:

1 century = 100 1 year =1February (3 1 day) has:1\ 3 \ 5 \ 7 \ 8 \1.

Abortion (30 days) includes: 4\6\9\ 1 1, February 28th in a normal year and February 29th in a leap year.

There are 365 days in a normal year and 366 days in a leap year.

1 day =24 hours 1 hour =60 minutes 1 minute =60 seconds 1 hour =3600 seconds.

The Complete Works of Mathematical Formulas in Primary Schools, Part III: Geometry.

1, squared

Circumference of a square = side length ×4 Formula: C=4a

Square area = side length × side length formula: s = a× a.

Cubic volume = side length × side length × side length formula: v = a× a× a.

2. Rectangular

The circumference of a rectangle = (length+width) ×2 Formula: C=(a+b)×2.

Area of rectangle = length× width formula: S=a×b

Cuboid volume = length× width× height formula: v = a× b× h.

3, triangle triangle area = bottom × height ÷2. Formula: S= a×h÷2

4. parallelogram area = base× height formula: s = a× h.

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

6. Diameter of circle = radius ×2 formula: d=2r radius = diameter ÷2 formula: r= d÷2.

Circumference = π× diameter formula: c=πd =2πr Area of circle = radius× radius× π formula: S=πrr

7. Cylinder

Transverse area of cylinder = bottom circumference × height. Formula: S=ch=πdh=2πrh.

Surface area of cylinder = perimeter of bottom × height+area of circles at both ends. Formula: S=ch+2s=ch+2πr2.

Total volume of cylinder = bottom area × height. Formula: V=Sh

8. Cone

Total volume of cone = bottom area × height × 1/3 formula: V= 1/3Sh.

The sum of the internal angles of the triangle = 180 degrees.

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

Perpendicular: Two straight lines intersect at right angles. Two straight lines like this,

Suppose these two straight lines are perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two straight lines is called the vertical foot.