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Key points of mathematics in grades one to six
① Appendix+Appendix = sum

And-one addend = another addend

(2) minuend = difference

Negative difference = negative

Difference+Minus = Minus

③ Factor × factor = product

Product ÷ One factor = another factor

(4) Divider = quotient

Dividend = divisor

Quotient × Divider = Divider

Divider × quotient+remainder = dividend

. compare

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

According to the meaning of the ratio, the ratio can be obtained; The method of comparison: divide the former by the latter term.

The basic nature of the ratio: the first and last items of the ratio are multiplied or divided by the same number (except 0), and the ratio remains unchanged. The basic properties of the ratio can be used to simplify the ratio.

Elementary arithmetic.

① Among the four operations, addition and subtraction are called primary operations, and multiplication and division are called secondary operations.

(2) If the formula without brackets only contains operations at the same level, it should be calculated from left to right once; If there are two levels of operation, do the second level operation first, and then do the first level operation.

(3) In the formula with brackets, the brackets should be counted first. If there are both brackets, count the brackets first, then the brackets, and finally the brackets.

39. Application of scores and percentages

The unit "1" is known and multiplied. The unit "1" is unknown. Use division.

(1) What percentage of a number is another number?

Basic formula: number before ÷ number after (comparison quantity ÷ standard quantity).

(2) What is a fraction or multiple of a number? (unit "1" is known)

Basic formula: quantity in "1" × score = quantity corresponding to the score.

(3) What is a fraction of a number? Find this number. (The unit "1" is divided or the equation is unknown. )

Basic formula: the quantity corresponding to the fractional rate ÷ the fractional rate = the quantity of the unit "1" or the solution of the column equation.

(4) Given two numbers, find out how many scores one number is more than the other.

Given two numbers, what percentage is one more than the other?

Given two numbers, find out how many points one number is less than the other.

Given two numbers, how much is one less than the other?

Basic formula: the difference between two numbers ÷ the quantity in the unit "1" (standard quantity

Principal: Money deposited in the bank is called principal. Interest: the excess money paid by the bank when withdrawing money is called interest. Interest rate: the percentage of interest in principal is called interest rate.

② Interest calculation formula: interest = principal × time × interest rate.

Interest tax = principal × time × interest rate ×5%

4 1. Four operating laws

Additive commutative law: A+B = B+A,

Additive associative law: (a+b)+c = a+(b+c)

Multiplicative commutative law: ab=ba,

Law of multiplicative association: (ab)c=a(bc)

Law of multiplication and distribution: (a b) c = AC BC

Operation attribute

① Basic properties of subtraction: A-(B+C) = A-B-C.

a-b-c=a-(b+c)

② the basic nature of division: a÷b÷c=a÷(b×c)

(a b)c = a \c b \c

1, the perimeter of the rectangle = (length+width) ×2 C=(a+b)×2.

2. The circumference of a square = side length ×4 C=4a.

3. Area of rectangle = length× width S=ab

4. Square area = side length x side length s = a.a = a.

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

6. parallelogram area = bottom x height S=ah

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

8. Diameter = Radius× 2D = 2r Radius = Diameter ÷2 r= d÷2

9. The circumference of a circle = π× diameter = π× radius× 2c = π d = 2π r.

10, circular area = pi × radius× radius? =πr

1 1, the surface area of a cuboid = (length× width+length× height+width× height) × 2.

12, cuboid volume = length× width× height V =abh.

13, the surface area of the cube = side length × side length× ×6 S =6a.

14, volume of cube = side length x side length x side length v = a.a.a = a.

15, lateral area of cylinder = circumference of bottom circle × height S=ch.

16, surface area of cylinder = upper and lower bottom area+side area.

s = 2πr+2πRH = 2π(d÷2)+2π(d÷2)h = 2π(c÷2÷π)+Ch

17, cylinder volume = bottom area × height V=Sh

V=πr h=π(d÷2) h=π(C÷2÷π) h

18, volume of cone = bottom area × height ÷3.

v = sh÷3 =πr h÷3 =π(d÷2)h÷3 =π(c÷2÷π)h÷3

19, cuboid (cube, cylinder)

1, number of copies × 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. Appendix+Appendix = 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

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. Cube V: volume A: side surface area = side length × side length× 6s table =a×a×6 volume = side length× side length× side length V = a× a× a.

3. rectangular

Perimeter area 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.

(1) Surface area (L× W+L× H+W× H) ×2

S=2(ab+ah+bh)

(2) Volume = length × width × height

V=abh

5 triangle

S area a bottom h height

Area = bottom × height ÷2

s=ah÷2

Height of triangle = area ×2÷ base.

Triangle base = area ×2÷ height

6 parallelogram

S area a bottom h height

Area = bottom × height s=ah

7 trapezoid

Height of upper bottom b and lower bottom h in s area a

Area = (upper bottom+lower bottom) × height ÷2

s=(a+b)× h÷2

8 laps

Area c perimeter d= diameter r= radius

(1) circumference = diameter ×∏=2×∏× radius

c =∏d = 2r

(2) area = radius × radius×∈

Cylinder 9

V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter

(1) lateral area = bottom circumference × height.

(2) Surface area = lateral area+bottom area ×2

(3) Volume = bottom area × height

(4) Volume = lateral area ÷2× radius.

10 cone

V: volume h: height s; Bottom area r: bottom radius

Volume = bottom area × height ÷3

Total number ÷ Total number of copies = average value

Sum-difference problem

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

And folding problems.

Sum \ (multiple-1) = decimal

Decimal × multiple = large number

(or sum-decimal = large number)

Difference problem

Difference ÷ (multiple-1) = decimal

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:

Number of plants = number of nodes+1 = total length-1.

Total length = plant spacing × (number of plants-1)

Plant spacing = total length ÷ (number of plants-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

Total length = plant spacing × number of plants

Plant spacing = total length/number of plants

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

Number of plants = number of nodes-1 = total length-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

Total length = plant spacing × number of plants

Plant spacing = total length/number of plants

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

Concentration problem

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 problem

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%)

Time unit conversion

1 century = 100 1 year =65438+ February.

The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.

Abortion (30 days) includes: April \ June \ September \165438+1October.

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 point = 60s 1 hour = 3600s product = bottom area × height V=Sh.