The People's Education Press summarizes the arrangement of mathematical concepts in the sixth grade of primary school 1 unit location 1. Find the location: first the column, then the row. The format is: (column, row). For example: (a, b). 2. Representation of position: ① brackets on both sides; 2. There is a comma in the middle; ③ Write columns first, then rows. 3. Translation method: translation from left to right, with the columns unchanged; Translation up and down, the rows change and the columns remain unchanged. Unit 2 fractional multiplication 1. The significance of fractional multiplication is the same as that of integer multiplication: finding the sum of several identical addends is a simple operation. For example: ++= × 3 (b 0) 2. The calculation rule of fractional multiplication by integer: fractional multiplication by integer, the product of fractional numerator multiplied by integer is numerator, and the denominator remains unchanged. For example, a × (a) = (For the sake of simplicity, if you can make an appointment, you must make an appointment first and then multiply. ) Note: When multiplying with fractions, you must first turn the fractions into false fractions before performing the operation. 3. Multiply the score by an integer; (1), a fraction multiplied by an integer can be regarded as the sum of several fractions. For example: ×n=++,,,, (b 0)②, an integer multiplied by a fraction can be regarded as finding the fraction of an integer. For example, n x means: what is the number of n? 4. Calculation rules of fractional multiplication: fractional multiplication, the product of molecular multiplication is numerator, and the product of denominator multiplication is denominator. For example: × = (b, d 0) Note: In order to simplify the calculation, you can divide the points first and then multiply them by 5. Two numbers whose product is 1 are called reciprocal. For example: × = 1, then the sum is the reciprocal. 6. How to find the reciprocal of a number (except 0): switch the numerator and denominator of this fraction. The reciprocal of 1 is 1. 0 has no reciprocal. The reciprocal of the true score is greater than1; The reciprocal of the false score is less than or equal to1; The reciprocal of the score is less than 1. Note: the reciprocal must be a pair of two numbers, and a single number cannot be called reciprocal 7. A number (except 0) is multiplied by a true fraction, and the product is less than itself. 8. Multiply a number (except 0) by a false fraction, and the product is equal to or greater than itself. 9. A number (except 0) times a fraction, and the product is greater than itself. 10. Related concepts for solving fractional multiplication application problems: ① Solutions to fractional multiplication application problems: Given a number, what is the score of this number? (2) the method of finding the unit "1": look for the key sentences with scores and pay attention to "de"; Rules after comparison ③ "increase", "improve" and "increase production" mean "more"; "Reduction", "decline" and "layoffs" mean "less"; The meanings of "equivalent", "accounted for", "yes" and "equal". ④ When the unit "1" in the key sentence is not obvious, it is necessary to complete the key sentence and supplement it with the form of "whose score is who" or "A is greater than B" or "A is less than B". Unit 3 Summary of the concept of fractional division 1. Significance of fractional division: The significance of fractional division is the same as that of integer division, and both are operations to find the other factor by knowing the product of two factors and one of them. For example, it means that the product of two numbers is known as one of the factors and what is the other factor. 2.① Dividing the score by an integer (except 0) is equal to multiplying the score by the reciprocal of this integer. For example: ÷c= × (a, c 0)② An integer divided by a fraction equals an integer multiplied by the reciprocal of this fraction. For example: c ÷ = c× (A 0) 3. The calculation rule of fractional division: A divided by B (except 0) equals the reciprocal of A multiplied by B. Division of two numbers is also called the ratio of two numbers. 5. ":"is a comparative symbol, pronounced "than". The number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison. The quotient obtained by dividing the former term by the latter term is called the ratio. For example: a: b = (a is the ratio of the previous paragraph; B is the last term of the ratio; It is a ratio, and the ratio is generally a fraction, which can be an integer or a decimal. ) 6. Method of comparison and simplification: You can use the former item and the latter item. For example: =(b, d 0) 8. Compared with division, the former term of ratio is equivalent to dividend, the latter term is equivalent to divisor, and the ratio is equivalent to quotient. For example: a: b = a ÷ b = (b 0). 9. According to the relationship between fraction and division, the former term of ratio is equivalent to numerator, the latter term is equivalent to denominator, and the ratio is equivalent to the value of fraction. For example: a: b = a ÷ b = (b 0). 10. The basic property of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged. For example: a: b = a: b = (b 0) 1 1. In industrial and agricultural production and daily life, it is often necessary to allocate a quantity according to a certain proportion. This method is usually called proportional distribution. 12, ① When a number (except 0) is divided by a true fraction, the quotient obtained is greater than itself. ② The quotient of a number (except 0) divided by a false fraction is less than or equal to itself. (3) When a number (except 0) is divided by a fraction, the quotient is less than itself.

16π = 50.24 36π = 1 13.04 64π = 200.96 96π = 30 1.44

4π =12.568π = 25.1225π = 78.513, the result of common square.

1 12 = 12 1 122

= 144 132

= 169 142

= 196 152

= 225 162

= 256 172

= 289 182

= 324 192

= 36 1

Unit 5 Percentage

First, the meaning and writing of percentage

1, meaning of percentage: indicates that one number is a percentage of another number.

Percentage refers to the ratio of two numbers, so it is also called percentage or percentage.

Percent is usually not written as a fraction, but as a percent sign "%",and the company name cannot be followed by a percentage.

2. One thousandth: indicates that one number is a thousandth of another number. 3, the main contact and difference between percentage and score:

(1) connection: both of them can express the ratio relation of two quantities. (2) the difference:

1. has different meanings: percentage only indicates the multiple ratio of two numbers, and cannot indicate the specific quantity, so it can't take units;

Fraction can represent both a specific number and the relationship between two numbers, and the specific number can be expressed in units.

② The percentage of molecules can be integers or decimals;

The numerator of a fraction cannot be a decimal, only a natural number other than 0.

(3) The percentage reading method is basically the same as the fractional reading method. The denominator is read first, and then the numerator. However, it should be noted that when reading the denominator of the percentage, you can't read a few percent, but only read "a few percent".

4, the percentage of writing: usually not written in the form of fractions, but after the original molecule to add "%"to indicate.

Second, the reciprocity of percentage and fraction and decimal (1) The reciprocity of percentage and decimal:

1, decimal percentage: the decimal point is moved to the right by two places, followed by hundreds of semicolons. 2. Decimal percentage: move the decimal point two places to the left and remove the percent sign at the same time.

(b) Percentage and score of reciprocity

1, percentage component number:

Divide the percentage into components first, and then rewrite the percentage into component number 100, which can be simplified to the simplest fraction. 2. Percentage of scores:

(1) Using the basic properties of the fraction, the denominator of the fraction is enlarged or reduced, and the fraction with the letter 100 is written as a percentage. (2) Convert fractions into decimals (except infinity, three decimals are usually reserved), and then convert decimals into percentages.

(3) The mutual transformation between common fractions and decimals and percentages.

2 1 = 0.5 = 50% 5 1 = 0.2 = 20% 85

= 0.625 = 62.5% 4 1 = 0.25 = 25% 52 = 0.4 = 40% 8 1

= 0. 125 = 12.5% 43 = 0.75 = 75% 53 = 0.6 = 60% 83

= 0.375 = 37.5% 16 1 = 0.0625 = 6.25% 54 = 0.8 = 80% 87

= 0.875 = 87.5% 25 1 = 0.04 = 4﹪ 252 = 0.08 = 8﹪ 253 = 0. 12 = 12﹪ 25

4 = 0. 16 = 16﹪ 3. Solve general application problems by percentage (1).

Common calculation methods of 1. percentage: ① qualified rate =

% 100? Number of qualified products ② Germination rate =% 100? Total number of seeds Number of seeds germinated

③ Attendance rate =

% 100? Total number of people, attendance ④ Compliance rate =% 100? Total number of students

Number of students who meet the standard

⑤ Survival rate =

% 100? Total survival ⑥ flour yield =% 100? Weight of powder; The weight of the powder.

⑦ Drying speed =

% 100? Weight before drying; Weight after drying; Water content before drying =% 100 weight.

Weight after drying

Weight before drying

Generally speaking, attendance, survival rate, qualified rate and correct rate can reach 100%, rice yield and oil yield can not reach 100%, and the completion rate and percentage increase can exceed 100%. (Generally, the powder yield is 70% and 80%, and the oil yield is 30% and 40%. ) 2. Knowing the quantity of the unit "1" (by multiplication), find the percentage of the unit "1": the relationship between quantity and fractional multiplication is the same:

(1) is "Yes" before the score: the amount of unit "1" × the amount corresponding to the score (2) means "more or less" before the score: the amount of unit "1 "× (1? Fraction) = the number corresponding to the fraction.

3. The quantity of the unit "1" is unknown (by division). What percentage is the known unit "1"? The company "1" was found.

Solution: (suggestion: it is best to solve it by equation)

Equation (1): Let the unknown quantity be x according to the quantitative relation and solve it by equation.

(2) Arithmetic (division): the amount corresponding to the score ÷ the corresponding score = the amount of the unit "1".

4. What percentage is one number more (less) than another?

The difference between two numbers ÷ "1"×100% or:

① Overfinding percentage: (large number ÷ decimal-1)× 100%② Underfinding percentage: (1- decimal ÷ large number )×100%.

(2) Discount

1. discount: a few percent of the original price is sold as a discount. Commonly known as "discount".

A few percent discount means a few tenths, that is, dozens of percent. For example, 20% off =

10

eight

= 80%, 65% off = 0.65 = 65% 2, 10% is one tenth, that is, 10%. 35% is 3.5%, which means 35%.

A few percent is a few tenths, that is, dozens of percent. For example, 50% means ()%

"Discount" refers to the degree of price reduction of commodities. A 75% discount means that the current price is ()% of the original price.

(3) Paying taxes

1, tax payment: tax payment is to pay part of the income of the collective or individual according to a certain proportion according to the relevant provisions of the national tax law.

To the country.

2. The significance of tax payment: tax payment is one of the main sources of national fiscal revenue. The state uses the collected taxes to develop economy, science and technology, education, culture and national defense security. 3. Taxable amount: The tax paid is called taxable amount. 4. Tax rate: The ratio of taxable amount to various incomes is called tax rate. 5. Calculation method of tax payable: tax payable = total income × tax rate

(4) Interest

1. Deposits are divided into demand, lump-sum deposit and withdrawal and lump-sum deposit and withdrawal.

13

2. The significance of saving: People often deposit temporarily unused money in banks or credit cooperatives, which can not only support the elderly.

National construction also makes personal money safer and more planned, and can also increase some income.

3. Principal: Money deposited in the bank is called principal.

4. Interest: The excess money paid by the bank when withdrawing money is called interest. 5. Interest rate: The ratio of interest to principal is called interest rate. 6. Calculation formula of interest: interest = principal × interest rate × time.

7. Note: If you want to pay interest tax (interest on national debt and education deposits is not taxed), then:

After-tax interest = interest-taxable interest amount = interest-interest× interest tax rate = interest× ×( 1- 0/-interest tax rate) 8. Principal and interest = principal+interest.

Unit 6 Statistics

First, the meaning of the pie chart:

The total number is expressed by the area of the whole circle, and the relationship between the number of parts and the total number is expressed by the area of each sector in the circle. That is, the percentage of each part in the total (so it is also called percentage chart). Second, the advantages of commonly used statistical charts:

1, bar chart: you can clearly see the quantity of various quantities.

2. Broken line statistical chart: We can not only see the number of various quantities, but also clearly see the increase and decrease of the quantity. 3. Department chart: It can clearly reflect the relationship between the quantity of each part and the total.

Third, the size of the sector: in the same circle, the size of the sector is related to the size of the central angle of the sector, which

The bigger the fan, the bigger the fan. (So the percentage of the sector area to the circle area is the percentage of the central angle of the sector to the peripheral angle. )

Unit 7 Mathematics Wide Angle

First, the characteristics of the problem of "chickens and rabbits in the same cage":

There are two or more unknowns in the topic, and it is required to find a single quantity of each unknown according to the total amount.

The second is to solve the problem of "chickens and rabbits in the same cage"

1, guessing method

2. Hypothetical method

(1) If they are all rabbits (2) If they are all chickens.

(3) the ancient "foot lifting method":

If every chicken and rabbit raises half a foot, then every chicken will become a "chicken with one leg" and every rabbit will become a "rabbit with two legs". In this way, the total number of feet of chickens and rabbits is reduced by half. This way of thinking is called reduction. Relationship: total number of chickens and rabbits ÷2- total number of chickens and rabbits = number of rabbits; Total number of chickens and rabbits-number of rabbits = number of chickens.

~ If you agree with my answer, please click the "Adopt as Satisfied Answer" button in time ~

~ mobile phone questioner is satisfied with the evaluation point in the upper right corner of the client.

~ Your adoption is my motivation ~ ~

~ If you have any new questions, please don't send them in the form of questions. Send me another question for help or send the question link address at the place where the question is asked. It's hard to answer, please forgive me ~ ~

O(∩_∩)O, remember to praise adoption, help each other, and wish you progress in your studies!

/link? URL = wfyuij920N7Segan01P8Yruigmhnchxha1T7Ikdeglrvgnshautkps-Lezxiukwy9Utpuxivpdpynweo3-2ZS8 WWJS431RV-5K-YXE This website will be cleaner. I wish you progress in your study!