Complete set of mathematical formulas

Definition, Theorem and Formula of Necessary Memory

Area of triangle = base × height ÷2. The formula S= a×h÷2.

Square area = side length × side length formula S= a×a

Area of rectangle = length× width Formula S= a×b

Area of parallelogram = base× height Formula S= a×h

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

Sum of internal angles: sum of internal angles of triangle = 180 degrees.

Cuboid volume = length× width× height formula: V=abh

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

Volume of cube = side length × side length × side length formula: V=aaa.

Circumference = diameter × π formula: L = 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

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.

The law of division of fractions: dividing by a number is equal to multiplying the reciprocal of this number.

Reading comprehension will apply the following formulas that define the properties of theorems.

First of all, arithmetic.

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 and the degree of the unknown number 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. ..

As far as the calculation formula of quantitative relationship is concerned

1, unit price × quantity = total price

2. Single output × quantity = total output

3. Speed × time = distance

4. Work efficiency x time = total workload.

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

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

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

Frequency divider/frequency divider = frequency divider = frequency divider/frequency divider = quotient × frequency divider

Division with remainder: dividend = quotient × divisor+remainder

A number is divided by two consecutive numbers. You can multiply the last two numbers first, and then divide this number by their product, and the result is still the same. For example: 90 ÷ 5 ÷ 6 = 90 ÷ (5× 6)

6. 1 km = 1 km 1 km =1000m

1 m = 10 decimeter 1 decimeter =10 cm1cm =10 mm.

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

1 cm2 = 100 mm2

1 m3 = 1000 cubic decimeter

1 cm3 = 1000 cm3

1 ton = 1 000kg1kg = 1 000g = 1 kg =1kg.

1 hectare = 1 10,000 square meters. 1 mu = 666.666 square meters.

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

7. 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.

8. What is proportion? Two formulas with equal ratios are called proportions. For example, 3: 6 = 9: 18

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

10, solution ratio: the unknown term in the ratio is called the solution ratio. Such as 3: χ = 9: 18.

1 1, ratio: 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 be) or kx = y.

12, inverse ratio: two related quantities, one changes and the other changes. If the product of two corresponding 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.

Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages.

13. To convert decimals into percentages, just move the decimal point to the right by two places and add hundreds of semicolons. 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.

14. When a fraction is converted into a percentage, it is generally converted into a decimal (except for the inexhaustible, three decimal places are generally reserved), 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%.

Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.

15, learn decimal component numbers and fractions to decimals.

16, 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. )

17, prime number: the common divisor is only 1 two numbers, which is called prime number.

18, least common multiple: the multiple shared by several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.

19. Comprehensive score: dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called comprehensive score. (Common divisor is the least common multiple)

20. Approximation: It is called approximation to change a fraction into a fraction equal to it, but with smaller numerator and denominator. (The greatest common divisor is used for divisor)

2 1, simplest fraction: The fraction whose numerator and denominator are prime numbers is called simplest fraction.

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

Numbers in units of 0, 2, 4, 6 and 8 can all be divisible by 2, that is, they can be subtracted 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.

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

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

24. 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.

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

29. 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.

30. Natural number: An integer used to represent the number of objects is called a natural number. 0 is also a natural number.

3 1, Cyclic Decimal: a decimal, starting from a certain digit in the decimal part, and one or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14.

32. Acyclic decimals: Decimals that start from the decimal part without one or several numbers appearing repeatedly in turn. Such a decimal is called an acyclic decimal.

Like 3. 14 1592654.

33. Infinitely circulating decimal: a decimal, from the decimal part to the infinite digits, is called an infinitely circulating decimal without one or several numbers appearing repeatedly in turn. Such as 3. 14 1592654. ...

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

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

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 = sum-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 ×4 C=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

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 = bottom × height ÷2 s=ah÷2

Height of triangle = area ×2÷ base of triangle = area ×2÷ height

6 parallelogram s area a bottom h height

Area = bottom × 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

Circumference = 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× high surface area = lateral area+area of bottom× 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