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 additive combination: 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. 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 by any number that is not.
Simple multiplication: multiplication of multiplicand and multiplier with O at the end. 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 at the same time, 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? A: An equation with an unknown number of degree 1 is called a linear equation with one variable.
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: addition and subtraction of fractions with denominator, only numerator addition and subtraction, denominator unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12. Comparison of fractional sizes: Compared with the 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 multiplication of the fraction and the integer is the numerator, and the denominator remains unchanged.
14. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is 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 the false fraction as an integer, and the true fraction 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) is equal to 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. 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 expressions with equal ratios are called proportions. For example, 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: Finding the unknown item 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 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×y = k( k must be) or k/x = y.
28. Percentage: The number that indicates 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 converted into a decimal (except infinity, three decimal places are usually reserved), and then 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.
33. Learn how to divide scores into scores and how to divide scores into scores.
34. Common divisor: Several numbers can be divisible by the same number at the same time. This number is called the common divisor of these numbers. (or the common divisor of several numbers is called the common divisor of these numbers. One of them is called the 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: 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. Approximate fraction: It is called approximate fraction to change a fraction into a fraction that is equal to it, but the numerator and denominator are relatively small. (Common divisor)
39. simplest fraction: The numerator and denominator are fractions of prime numbers, which are called simplest fraction. At the end of the score calculation, the score 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. Numbers in units of 0 or 5 can be divisible by 5, that is, they can be reduced 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 (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
45. Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 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 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 is called a 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 decimals: Decimals that start from the decimal part and do not have one or several numbers repeated. Such a decimal is called an 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 repeating in turn. Such as 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. For 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 cylinder: the surface area of 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