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Summary of Mathematics Knowledge Points in the Sixth Grade of Primary School (Part Two)
The following is my review materials.

65438+ 0× number of copies per copy = total

Total copies/number of copies = number of copies

Total copies/number of copies = number of copies

2 1 multiple × multiple = multiple

Multiply1Multiply = Multiply

Multiply/Multiply = 1 Multiply

3 Speed × Time = Distance

Distance/speed = time

Distance/time = speed

4 unit price × quantity = total price

Total price/unit price = quantity

Total price ÷ quantity = unit price

5 Work efficiency × working hours = total workload.

Total amount of work ÷ work efficiency = working hours

Total workload ÷ working time = working efficiency

6 addend+addend = sum

And-one addend = another addend

7 minuend-minuend = difference

Negative difference = negative

Difference+Minus = Minus

8 factor × factor = product

Product ÷ One factor = another factor

Dividend = quotient

Dividend = divisor

Quotient × Divider = Divider

Calculation formula of mathematical graphics in primary schools

1 square

Perimeter area side length

Perimeter = side length ×4

C=4a

Area = side length × side length

S=a×a

2 cubic meters

Volume a: edge 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

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) Transverse 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

Formula of sum and difference problem

(sum+difference) ÷ 2 = large number

(sum and 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) Elementary School Olympiad Formula

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)

Formula of differential multiple problems

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

Tree planting formula

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

Formula of profit and loss problem

(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.

The formula of encounter problem

Meeting distance = speed × meeting time

Meeting time = meeting distance/speed and

Speed Sum = Meeting Distance/Meeting Time

The formula for tracing 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

Formula of 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 formula 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%)

References:

Baidu Knows

(1) Number of readings 1.

How to read integers: from high to low, read step by step. When reading the 110 million level, first read according to the reading method of the 100 million level, and then add a word "100 million" or "10 thousand" at the end. The zeros at the end of each stage are not read, and only a few zeros of other digits are read.

2. Writing of integers: from high to low, writing step by step. If there is no unit on any number, write 0 on that number. 3.

Decimal reading: when reading decimals, the integer part is read by integer reading method, the decimal point is read as "dot", and the decimal part reads the numbers on each digit from left to right in turn. 4.

How to write decimals: When writing decimals, the integer part is written as an integer, the decimal point is written in the lower right corner of each digit, and the decimal part is written on each digit in sequence. 5.

How to read fractions: When reading fractions, read the denominator first, then the "fraction", and then the numerator. Both numerator and denominator are integers. 6. How to write the fraction: write the fraction first, then the denominator, and finally the numerator and the integer.

7. Reading method of percentage: When reading percentage, read the percentage first, and then read the number before the percentage symbol. When reading, read it as an integer. 8.

Writing of percentage: percentage is usually expressed by adding a percent sign "%"after the original molecule instead of a fraction.

(2) The number of rewrites

In order to facilitate reading and writing, a large multi-digit number is often rewritten as a number in units of "10,000" or "100 million". Sometimes, if necessary, you can omit the number after a certain number and write it as an approximation. 1.

Accurate numbers: In real life, for the convenience of counting, larger numbers can be rewritten as numbers in tens of millions or hundreds of millions. The rewritten number is the exact number of the original number. For example, put 1254300000.

The number rewritten in ten thousand years is 6.5438+0.2543 million; Rewritten into a number of 65.438+025.43 billion in units of hundreds of millions. 2.

Approximation: According to actual needs, we can also use a similar number to represent a larger number, omitting the mantissa after a certain number. For example: 13024900 15 The mantissa after omitting 100 million is1300 million. 3.

Rounding method: if the highest digit of mantissa to be omitted is 4 or less, the mantissa is removed; If the digit with the highest mantissa is 5 or more, the mantissa is truncated and 1 is added to its previous digit. For example, omit

The mantissa after 34.59 million is about 350 thousand. After omitting 472509742 billion, the mantissa is about 4.7 billion. 4. Size comparison 1.

Compare the sizes of integers: compare the sizes of integers, and the number with more digits will be larger. If the numbers are the same, view the highest number. If the number in the highest place is larger, the number is larger. The number in the highest bit is the same. Just look at the next bit, and the bigger the number, the bigger it is.

2.

Compare the sizes of decimals: look at their integer parts first, and the numbers with larger integer parts will be larger; If the integer parts are the same, the tenth largest number is larger; One tenth of the numbers are the same, and the number with the largest number in the percentile is the largest. ...

3. Compare the scores: the scores with the same denominator and the scores with large numerator are larger; For numbers with the same numerator, the score with smaller denominator is larger. If the denominator and numerator of a fraction are different, divide the fraction first, and then compare the sizes of the two numbers. (3) the number of mutual

1. Decimal component number: There are several decimals, so writing a few zeros after 1 as denominator and removing the decimal point after the original decimal point as numerator can reduce the number of quotation points. 2.

Fraction to decimal: numerator divided by denominator. Those that are divisible are converted into finite decimals, and some that are not divisible are converted into finite decimals. Generally three decimal places are reserved. 3.

A simplest fraction, if the denominator does not contain other prime factors except 2 and 5, this fraction can be reduced to a finite decimal; If the denominator contains prime factors other than 2 and 5, this fraction cannot be reduced to a finite decimal. 4.

Decimal to percentage: Just move the decimal point to the right by two places and add hundreds of semicolons at the end. 5. Decimal percentage: Decimal percentage, just remove the percent sign and move the decimal point two places to the left. 6.

Fractions are converted into percentages: Fractions are generally converted into decimals first (three decimal places are usually reserved when they are not used up), and then decimals are converted into percentages. 7. Decimalization of percentage: First, rewrite percentage into component quantity and put forward a quotation that can be simplified to the simplest score.

(4) The divisibility of a number is 1. Divide a composite number into prime factors, usually by short division. Divide this complex number by a prime number until the quotient is a prime number, and then write the divisor and quotient in the form of multiplication. 2.

The way to find the greatest common divisor of several numbers is to divide them continuously until the quotient obtained is only the common divisor of 1, and then multiply all the divisors to get the product, which is the greatest common divisor of these numbers.

3.

The way to find the least common multiple of several numbers is to divide the common divisor of these numbers (or part of them) until it is coprime (or pairwise coprime), and then multiply all the divisors and quotients to get the product, which is the least common multiple of these numbers.

4. Two numbers that become coprime relations: 1 and any natural number coprime; Two adjacent natural numbers are coprime; When the composite number is not a multiple of the prime number, the composite number and the prime number are coprime;

When the common divisor of two composite numbers is only 1, these two composite numbers are coprime. (5) Divide method and general divide method: use the common divisor of numerator and denominator (except 1) to remove numerator and denominator; Usually, we have to separate it until we get the simplest score.

General division method: first find the least common multiple of the denominator of the original fraction, and then turn each fraction into a fraction with this least common multiple as the denominator.

decimal

The meaning of 1 decimal divides the integer 1 into 10, 100, 1000 ... one tenth, percentage, one thousandth ... can be expressed in decimal.

One decimal place indicates a few tenths, two decimal places indicate a few percent, and three decimal places indicate a few thousandths. ...

Decimal system consists of integer part, decimal part and decimal part. The point in the number is called the decimal point, the number to the left of the decimal point is called the integer part, and the number to the right of the decimal point is called the decimal part.

In decimals, the series between every two adjacent counting units is 10. The propulsion rate between the highest decimal unit "one tenth" of the decimal part and the lowest unit "one" of the integer part is also 10. 2 Classification of decimals

Pure decimals: Decimals with zero integer parts are called pure decimals. For example, 0.25 and 0.368 are pure decimals. With decimals: decimals whose integer part is not zero are called with decimals. For example: 3.25,

5.26 is all decimal. Finite decimals: The digits in the decimal part are finite decimals, which are called finite decimals. For example, 4 1.7, 25.3 and 0.23 are all finite decimals.

Infinite decimal: The digits in the decimal part are infinite decimal, which is called infinite decimal. For example: 4.33...3. 145438+05926 ...

Infinite acyclic decimal: the decimal part of a number with irregular arrangement and unlimited digits. Such decimals are called infinite cyclic decimals. For example: ∈

Cyclic decimal: the decimal part of a number, in which one or several numbers appear repeatedly in turn, is called cyclic decimal. For example: 3.555 … 0.0333 …12.15438+009 …

The decimal part of cyclic decimal is called the cyclic part of cyclic decimal. For example, the periodic part of 3.99 ... is "9", while the cyclic segment is 0.5454 ... is "54".

" 。 Pure cyclic decimal: the cyclic segment starts from the first digit of the decimal part, which is called pure cyclic decimal. For example: 3.111.5656 ...

Mixed cycle decimal: the cycle section does not start from the first digit of the decimal part. This is called mixed cyclic decimal. 3. 1222 …… 0.03333 ……

When writing a cyclic decimal, for simplicity, the cyclic part of the decimal only needs one cyclic segment, and a dot is added to the first and last digits of this cyclic segment. If the loop part only has

A number, just click on a point on it. For example: 3.777 ... Jane writing 0.5302302 ... Jane writing.

mark

The meaning of the fraction of 1 divides the unit "1" into several parts on average, and the number representing such one or several parts is called a fraction.

In the score, the middle horizontal line is called the dividing line; The number below the fractional line is called the denominator, indicating how many copies the unit "1" is divided into on average; The number below the fractional line is called the numerator, indicating how many copies there are.

Divide the unit "1" into several parts on average, and the number representing one part is called fractional unit. 2 Classification of Fractions True Fractions: Fractions with numerator less than denominator are called true fractions. The true score is less than 1.

False fraction: Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1. With fraction: False fraction can be written as a number consisting of integer and true fraction, which is usually called with fraction. 3 Reduction and comprehensive score

Changing a fraction into a fraction equal to it, but with smaller numerator and denominator, is called divisor. The denominator of a numerator is a fraction of a prime number, which is called simplest fraction.

Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.

(4) Percentage 1 indicates that one number is the percentage of another number, which is called percentage, also called percentage.

Or percentage. Percentages are usually expressed as "%". The percent sign is a symbol indicating percentage.