Unit 1: Understanding Negative Numbers

0 is neither positive nor negative, positive is greater than 0 and negative is less than 0.

Unit 2: Calculation of Polygon Area

1, a parallelogram can be divided into two identical triangles; Two identical triangles can form a parallelogram. A parallelogram can be divided into two identical trapezoids; Two identical trapezoids can form a parallelogram. The areas of triangles with equal bases and equal heights are equal; The area of a triangle is half that of a parallelogram with equal base and equal height.

2. The area of parallelogram = base × height (S represents the area of parallelogram, and A and H represent the base and height of parallelogram respectively, and the formula can be written as: S = a h).

3. The area of the triangle = base × height ÷2 (S is used to represent the area of the triangle, and A and H are used to represent the base and height of the triangle respectively, and the formula can be written as: S = a h÷2).

4. The area of trapezoid = (upper bottom+lower bottom) × height÷ 2 (S is used to represent the area of parallel trapezoid, and A, B and H are used to represent the upper bottom, lower bottom and height of parallelogram respectively, and the formula can be written as: S = (a+b) h÷2).

Unit 3: Understanding Decimals

Fractions with denominators of 1, 10, 100, 1000 can be expressed in decimals, with one decimal place representing a few tenths, two decimals representing a few percent and three decimals representing a few thousandths. ...

2. The first digit to the right of the decimal point is ten digits, and the counting unit is one tenth (0.1); The second digit to the right of the decimal point is the percentile, and the counting unit is one percent (0.01); The third digit to the right of the decimal point is one thousandth, and the counting unit is one thousandth (0.001); The propulsion rate between every two adjacent counting units is 10.

3. Add 0 or remove 0 at the end of the decimal, and the size of the decimal remains the same, which is the essence of the decimal. According to the nature of decimals, decimals can usually be simplified by removing the 0 at the end of decimals.

4. To rewrite a number into a number with "ten thousand" as the unit, just add a decimal point in the lower right corner of this ten thousand digit, and then add the word "ten thousand" at the end of the number. To rewrite a number into a number with "100 million" as the unit, just add a decimal point to the lower right corner of this billion bit, and then add the word "100 million" at the end of the number.

Unit 4: Decimal addition and subtraction

1, the calculation method of decimal addition and subtraction: the same number is aligned; From the lowest point: you must enter one at the age of ten or above; If the reduction is not enough, borrow 10 from the previous one and then reduce it.

For example:

2. The arithmetic of integer addition is also applicable to decimals.

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

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

Subtraction property: a-b-c=a-(b+c)

Unit 5: Looking for the Law

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Unit 6: Strategies to Solve Problems

1, when the perimeter of a rectangle is constant, the greater the difference between length and width, the smaller the area of the rectangle; The smaller the length-width difference, the larger the area of this rectangle.

2. When the area of a rectangle is constant, the greater the difference between length and width, the longer the perimeter of the rectangle; The smaller the difference between length and width, the shorter the circumference of this rectangle.

3. The length+width of the rectangle = half the circumference of the rectangle.

Unit 7: Fractional Multiplication and Division (1)

1, multiply a decimal by 10, 100, 1000 ... just move the decimal point of this decimal by one, two or three places to the right ...; Move the decimal point to the right by one, two or three places ... This decimal point is enlarged by 10 times, 100 times and 1000 times.

2|, divide a decimal by 10, 100, 1000. Just move the decimal point of this decimal to the left by one, two, three ...; Move the decimal point to the left by one, two or three places ... This decimal point is reduced by 10 times, 100 times and 1000 times.

3. If the dividend is constant, if the divisor is enlarged (or reduced) several times, the quotient will be reduced (or enlarged) by the same multiple; If the dividend remains the same, the quotient will be enlarged (or reduced) by the same multiple. Dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged.

Unit 8: hectares and square kilometers

Measure and calculate the land area, usually in hectares. Square land with side length 100 m and area 1 hectare. Measure and calculate a large area of land, usually in square kilometers. A square piece of land with a side length of 1 000m and an area of1km2. 1 hectare = 1 ten thousand square meters, 1 square kilometer = 100000 square meters = 100000 hectares.

Unit 9: Fractional Multiplication and Division (2)

1. The calculation algorithm of decimal multiplication is calculated according to the calculation method of integer multiplication.

2. Observe the decimal places in the factor * * *(factor * * *) and count the same decimal places from the right side of the product. When calculating the decimal point in the product, if there are not enough digits, you should add 0 in front. For example:

0 .07 8 4

3. The calculation method of fractional division: according to the principle of quotient invariance, the divisor is converted into an integer, and then it is calculated according to the calculation method of integer division.

4. The decimal point of quotient should be aligned with the decimal point of dividend;

5. If there is a remainder, you can continue the division by filling in zeros according to the nature of the decimal.

Multiply a nonzero number by a number less than 1, and this number will be smaller than the original one. For example:160× 0.05 = 8 48× 0.5 = 24 89× 0.1= 8.9 20× 0.25 = 5.

6. Decimals are called cyclic decimals, in which one or more numbers are repeated from a certain position in the decimal part. One or more numbers that appear repeatedly in turn are the cyclic part of this cyclic decimal. Such as: 2.55656 .....

Unit 10 Statistics

Total number of men and women

Total 39 18 2 1

Model airplane team 14 8 6

Folk music groups 8 3 5

Calligraphy group 7 3 4

Art group 10 4 6

The sixth grade mathematics knowledge point book 1

χ Unit 1: Equation

1 aхb = c 2 aх\b = c 3 aх+bх= c

Such as: 6х+5=23 2х÷5=4 2x+3x= 10.

Solution: 6 х+5-5 = 23-5 Solution: 2х=4×5 Solution 5x= 10.

6х= 18 2х=20 x= 10÷5

х= 18÷6х= 20÷2 x = 2

Х=3 х= 10

4. The key to solving application problems with equations is to find out the equivalent relationship in the problem.

For example, the height of a big tree is 64 meters, which is 22 meters less than that of a small tree. How many meters is the height of a small tree? (height of small trees × 2-22 = height of big trees)

Unit 2: Fractional Multiplication and Fractional Division

1, how many fractions are found, which can be calculated by addition or multiplication. By multiplication, the integer numerator is multiplied by the numerator, and the denominator remains the same, so that the result can be simplified.

How much is three? × 3 =+= or× 3 = =

2. Find the fraction of a number, which can be calculated by multiplication. Fraction multiplied by fraction is to use the product of molecular multiplication as the numerator and the product of denominator multiplication as the denominator, and the result can be simplified.

how much is it? × = = =

3. Two numbers whose product is 1 are reciprocal. For example, sum is the reciprocal, which can also be said to be the reciprocal. For example: × = 1

4. The number A divided by the number B (except 0) is equal to the reciprocal of the number A multiplied by the number B..

For example: ÷ 2 =× = =

5. The operation order of the elementary arithmetic of fractions is the same as that of the elementary arithmetic of integers.

Unit 3: Bi

1, meaning of ratio a: the ":"in b is the ratio symbol, the number a before the ratio symbol is called the previous term of the ratio, and the number b after the ratio symbol is called the latter term of the ratio. The ratio of two numbers represents the quotient ratio obtained by dividing two numbers and dividing the first term by the second term.

Such as: ratio ratio

3 : 5 =

The former term of the ratio is the latter term of the ratio.

2. The ratio of two numbers can be written in the form of division or fraction. The connections and differences between the three are as follows:

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The ratio area after the previous ratio sign.

The relationship between two numbers

Divisor quotient operation of divisor symbol.

Fraction numerator fraction line denominator decimal value a number

3. The basic nature 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, which is the basic property of the ratio.

4. Changing a ratio that is not an integer ratio into an integer ratio, and then changing a ratio that is not the simplest integer ratio into the simplest integer ratio is called a simplified ratio. For example:

30: 20 = (30 ÷10): (20 ÷10) (divided by the greatest common divisor)

= 3: 2 (the simplest integer ratio)

2.4: 3.6 = (2.4× 5): (3.6× 5) (Decimals are converted into integers)

= 12: 18

= (12 ÷ 6): (18 ÷ 6) (divided by the greatest common divisor)

= 2: 3 (the simplest integer ratio)

: = × 6 :× 6 (multiplied by the least common multiple of denominator)

= 2: 3 (the simplest integer ratio)

Unit 4: Percentage

1, the meaning of percentage. A number indicating that one number is a percentage of another number is called percentage, also called percentage or percentage, and the percent sign is "%".

For example, 32.5% is pronounced as 32.5%.

2. The difference between percentage and score: different meanings; Different symbols; Fractions can be used as both fractions and quantities, while percentages are fractions, not quantities, and cannot be followed by units.

3. Conversion between percentages and decimals.

Decimal percentage: remove the% sign and move the decimal point to the left by two places, for example, 78%=0.78.

Decimal to percentage: the decimal point moves two places to the right, followed by a percent sign.

Such as: 1.02= 102%

4. Conversion between percentage and score.

Fractions are converted into percentages, numerator is divided by denominator to get decimals, and then fractions are converted into percentages. For example: =4÷5=0.8=80%

Percent fraction, written in the form of fraction, and then simplified, for example: 20%= =

5. Find the percentage of one number to another, for example, A is 30, B is 50, A is B? For example: 30÷50=0.6=60%

6, the significance of various percentages:

Attendance = attendance/attendance rate × 100%

Rice yield = rice quantity/rice quantity × 100%

Qualified rate = number of qualified people ÷ total number × 100%

Unit 5: Substitution and hypothesis is to turn complex problems into simple ones.

1, replace. The price of pen is three times that of pencil.

Strategy: Replace pens with 3 pencils, or replace 3 pencils with 1 pen.

2. suppose. For example, apples are per kilogram1/yuan, pears are per kilogram in 8 yuan, * * * bought apples and pears1/kg, and * * spent 100 yuan. How many kilograms did you each buy?

Strategy 1: Assuming that each kilogram of pears is also 1 1 yuan, there is.

11×1-100 = 21(yuan)

21(11-8) = 7 (kg)

Strategy 2: Assuming that every kilogram of apples is also 8 yuan, there will be.

100-11× 8 =12 (yuan)

12 (11-8) = 4 (kg)

Unit 6: Possibility

Unit 7: Space and Graphics

1. Features of a cuboid: a cuboid has 6 faces, 12 sides and 8 vertices. The corresponding faces are exactly the same, and the opposite sides are equal in length. When you look at a cuboid from different angles, you can see at most three faces at the same time.

2. Features of the cube: the cube has 6 faces, 12 sides, each face of the cube is the same square, and 12 sides are equal.

3. Surface area: The total area of six faces of a long (regular) cube is called its surface area.

The total area of six faces of a (1) cuboid (cube) is called its surface area, and the unit of surface area is "square".

(2) cuboid surface area = (length× width+length× height+width× height) ×2

The letter S=2(ab+ah+bh).

Surface area of cube = side length × side length ×6

Is S=6a a letter?

4, volume and volume

(1), the size of the space occupied by an object is called the volume of the object. Commonly used unit of volume has cubic centimeters (cm? ), cubic decimeter (dm? ), cubic meters (m? )。 1 m3 = 1000 cubic decimeter, 1 cubic decimeter = 1000 cubic centimeter.

(2) The volume of an object that can be held in a container is called the volume of this container. The commonly used unit of volume are liters and milliliters. 1L = 1000ml， 1 decimeter = 1L = 1000ml， 1ml = 1cm。

(3) cuboid volume = length × width × height

Volume of cube = side length × side length × side length

Volume of cuboid (cube) = bottom area × height

(4) The calculation method of the volume of a long (regular) cube is the same as that of the volume, but the length should be the inner edge.