Location of the first unit:

1, find the position: first column, then row. The format is: (column, row). For example: (a, b).

2. Representation method of position: brackets on both sides, comma in the middle, column first, then row.

3. Translation method: translation from left to right, with line breaks in each column unchanged; Translation up and down, the rows change and the columns remain unchanged.

Unit 2 Fractional Multiplication:

1, the meaning of decimal multiplication is the same as that of integer multiplication: finding the sum of several identical addends is a simple operation.

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.

3. Integer multiplied by fraction: Fraction multiplied by integer can be regarded as the sum of several fractions. An integer multiplied by a fraction can be regarded as finding the fraction of an integer.

4. Calculation rules of fractional multiplication: fractional multiplication, the product of molecular multiplication is numerator, and the product of denominator multiplication is denominator.

5. Two numbers whose product is 1 are called 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.

7, a number (except 0) multiplied by a true fraction, the product is less than itself.

8, a number (except 0) multiplied by a false fraction, the product is equal to or greater than itself.

9, a number (except 0) multiplied by a fraction, the product is greater than itself.

Unit 3 Fractional Division:

1, the meaning of fractional division: the meaning of fractional division is the same as that of integer division, which is the operation of finding the other factor by knowing the product of two factors and one of them.

2. Fraction divided by integer (except 0) is equal to fraction multiplied by the reciprocal of the integer.

3. An integer divided by a fraction equals an integer multiplied by the reciprocal of this fraction.

4. Calculation rule of fractional division: A divided by B (except 0) equals the reciprocal of A multiplied by B..

5. The division of two numbers is also called the ratio of two numbers.

6. ":"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.

7. Comparison with division: the former term of comparison is equivalent to dividend, the latter term is equivalent to divisor, and the ratio is equivalent to quotient.

8. 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.

9. The basic nature of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

10, 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.

1 1, a number (except 0) divided by a true fraction, the quotient is greater than itself.

12, a number (except 0) divided by a false fraction, the quotient is less than or equal to itself.

13, a number (except 0) divided by a band fraction, the quotient is less than itself.

Unit 4 circle

1. Definition of a circle: a curve graph on a plane.

2. Fold a circular piece of paper in half twice, and the crease intersects the point of the center of the circle, which is called the center of the circle. The center of the circle is generally represented by the letter O, and its distance to any point on the circle is equal.

3. Radius: The line segment connecting the center of the circle and any point on the circle is called radius. The radius is generally represented by the letter R. If the two feet of a compass are separated, the distance between the two feet is the radius of the circle.

4. The center of the circle determines the position of the circle and the radius determines the size of the circle.

5. Diameter: The line segment whose two ends pass through the center of the circle is called diameter. The diameter is usually indicated by the letter d.

6. In the same circle, all radii are equal and all diameters are equal.

7. The same circle has countless radii and countless diameters.

8. The diameter of the same circle is twice the radius, and the radius is half the diameter.

9. Circumference of the circle: The length of the curve around the circle is called the circumference of the circle, which is represented by "C".

10, the circumference of a circle is always greater than 3 times the diameter, and this ratio is a fixed number. We call the ratio of the circumference to the diameter of a circle π, which is expressed by the letter π. Pi is an infinite cyclic decimal. In the calculation, π≈3. 14 is taken.

1 1, the formula of the circumference of a circle: C=πd or c = 2 π r.

12. Area of the circle: The area occupied by the circle is called the area of the circle.

13. Draw the largest circle in a square, and the diameter of the circle is equal to the side length of the square.

14. Draw the largest circle in the rectangle, and the diameter of the circle is equal to the width of the rectangle.

15, a ring, the radius of the outer circle is r, the radius of the inner circle is r, and its area is S=πR? -πr？ Or S=π(R? -r？ )。

16, the circumference of the ring = the circumference of the outer circle+the circumference of the inner circle.

17, the circumference of a half circle is equal to the circumference of a half circle plus the diameter. The perimeter formula of a semicircle: c = π d ÷ 2+d or c = π r+2r.

18. How many times the radius of the same circle is enlarged or reduced, so is the diameter and circumference. And the area is expanded or reduced by the square of the multiple.

19. The radius ratio of two circles is equal to the diameter ratio and the perimeter ratio, and the area ratio is equal to the square of the above ratio.

20. The radius of the circle is increased by one centimeter, and the circumference is increased by 2π one centimeter;

2 1. If the diameter of the circle increases by one centimeter, the circumference will increase by one centimeter.

22. In the same circle, the central angle accounts for a fraction of the central angle, and its sector area accounts for a fraction of the circular area; The right arc occupies a small part of the circumference.

23. When the perimeters of rectangle, square and circle are equal, the area of circle is the largest and the area of rectangle is the smallest.

24. Axisymmetric figure: If a figure is folded in half along a straight line, the figures on both sides can completely overlap, and this figure is an axisymmetric figure. The straight line where the crease lies is called the symmetry axis.

25. Figures with only one axis of symmetry 1 are: angle, isosceles triangle, isosceles trapezoid, sector and semicircle.

26. A figure with only two axes of symmetry is a rectangle.

27. A figure with only three axes of symmetry is an equilateral triangle.

28. A figure with only four axes of symmetry is a square.

29. Figures with countless axes of symmetry are: circles and rings.

30. A straight line with a diameter is the symmetry axis of a circle.

Unit 5 Percentage

1, the definition of percentage: the number that represents the percentage of one number to another number is called percentage. Percentages are also called percentages or percentages.

2. Meaning of percentage: It means that one number is the percentage of another number. Percent indicates the proportional relationship between two numbers, not the specific quantity, and there is no unit name.

3. Percentages are usually not written in fractional form, but expressed by adding "%"after the original molecule. The molecular part can be a decimal or an integer, which can be greater than 100, less than 100 or equal to 100.

4. Method of converting decimals into percentages: To convert decimals into percentages, just move the decimal point two places to the right, followed by hundreds of semicolons; To convert a percentage into a decimal, just remove the percent sign and move the number two places to the left.

5. The method of conversion between percentage and fraction: To turn a fraction into a percentage, usually first turn the fraction into a decimal (keep three decimal places), and then turn the decimal into a percentage.

6. Percent the number of components, first rewrite the percentage into the number of components, and make a quotation that can be turned into the simplest score.

7. Percentage formula:

Pass rate = qualified number ÷ total number 100% germination rate = germination number ÷ total number 100%.

Attendance rate = attendance ÷ total number 100%

8. Taxable amount: The tax paid is called taxable amount.

9. Calculation of tax payable: tax payable = income x tax rate.

10. Principal: Money in the bank is called principal.

1 1. Interest: The excess money paid by the bank when withdrawing money is called interest.

12, interest rate: the ratio of interest to principal is called interest rate.

13, the calculation formula of debt interest: interest = principal × interest rate× time.

13. Principal and interest: The sum of principal and interest is called principal and interest.

Unit conversion:

1, length unit conversion

1 km =1000m1m =1decimeter/decimeter =10cm1m =10cm/kloc-.

2, area unit conversion

1 square kilometer = 100 hectare 1 0000 square meter 1 square meter = 100 square decimeter.

1 square decimeter = 100 square centimeter

3, the body (volume) product unit conversion

1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1 liter 1 cubic decimeter = 1000 cubic centimeter.

1 cm3 = 1 ml

4. weight unit conversion:1t =1000kg1kg =1000mg.

Operating rules:

1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged. a+b=b+a

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. Such as: A+B+C = A+C+B = A+(B+C)

3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged. ab=ba

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. Such as: a×b×c=a×c×b=a×(b×c)

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: (ab)×c=acbc

6. Addition and subtraction property: a number subtracts several numbers continuously, which can be rewritten as the sum of these numbers. Such as: a-b-c=a-(b+c)

7. The essence of multiplication and division: a number is divided by several numbers continuously, which can be rewritten as the product of multiplication of these numbers. a÷b÷c=a÷(b×c)

Extended data:

Math learning methods in the sixth grade of primary school

1, grab the class

The most important thing to study on weekdays is to study in class. Listen carefully, follow the teacher's ideas and summarize the mathematical thinking methods that the teacher has talked about.

2. Finish the homework with high quality

Not only the speed is high, but also the accuracy is high. When writing homework, if you repeat the same type of questions, you should pay more attention to speed and accuracy. You should think and summarize such questions every time you finish, so as to further improve yourself and the rules and skills of solving problems.

3. Think hard and ask more questions

For the laws and theorems given by teachers, we should not only know why, but also know why. For the teacher's explanation and the content of the textbook, we should ask questions to eliminate hidden dangers in learning.

4. Summarize and compare, and clear your mind.

It is necessary to summarize and compare the knowledge points. Every time you finish a chapter, you must go over the contents of this chapter in your mind, and classify and compare similar and confusing knowledge points to distinguish them.

Compare topics. It is very helpful to write down the wrong questions in homework or exam selectively and write down the matters needing attention on the side.

5. Do extracurricular exercises selectively.

There is not enough time after class, so when doing extracurricular exercises, you should be less and more precise, and reflect more.