1, two digits divided by one digit: divide by ten digits first, then divide by four digits, and the remainder of each division is less than the divisor.

Division can be tested by multiplication. No residue: quotient× divisor = dividend; Having a remainder: quotient × divisor+remainder = dividend

2. 10 one is ten, 10 ten is one hundred, 10 one hundred is one thousand, 10 one thousand is ten thousand.

3. From the right, the first place is a unit, the second place is ten, the third place is one hundred, the fourth place is one thousand, and the fifth place is ten thousand. Four digits consist of thousands, hundreds, tens and ones.

4. Four-digit writing: write from top to bottom, write a few digits, and write 0 if there are no digits.

How to read four digits: starting from the high place, there are 1 zeros in the middle or several zeros in succession, all of which are read-only, and none of the zeros at the end are read.

5, the size of the comparison number: different digits, more digits; The number of digits is the same as the thousand digits; A thousand is the same as a hundred; A hundred is the same as ten; Ten digits are the same before comparing sizes.

6. To accurately measure the weight of an item, please use a "scale" to weigh it. Weigh the weight of general goods, usually in kilograms; Lighter items are usually measured in grams. The kilogram is represented by the symbol "kg" and the gram is represented by the symbol "g". 1 kg =1000g.

7. Both a rectangle and a square have four sides and four corners, which are quadrangles.

The opposite sides of a rectangle are equal, and all four corners are right angles. All four sides of a square are equal, and all four corners are right angles. A square is a special rectangle.

The total length of a plane figure in one week is the perimeter.

Perimeter of rectangle =2 length +2 width or circumference of rectangle = (length+width) ×2.

Length of rectangle = perimeter ÷2- width of rectangle = perimeter ÷2- length

Perimeter of a square = side length ×4 side length of a square = perimeter ÷4

To cut the largest square in a rectangle, as long as the side length = width.

8. 24-hour timing method

Time words include: morning, morning, morning, noon, afternoon, evening, etc.

A, ordinary timing method →24-hour timing method:

Excluding the time, afternoon and evening should be+12.

B, 24-hour timing method → ordinary timing method:

If time is added, it should be-12 when it exceeds12.

C. To find the elapsed time, you can first unify the timing method, and then subtract the previous time from the later time to change the result into a time unit.

9. Observe objects. When you look at a long (regular) cube from different angles, you can see at most three faces.

10, understand the meanings of words such as "occasionally", "often", "possibly" and "definitely", and use these words as examples.

1 1, identification score.

Understand "average score".

The denominator is the same as the numerator, and the bigger the numerator, the greater the score; The same numerator is smaller than the denominator and the denominator is larger.

The first volume of the fourth grade

The relationship between the parts of addition; One addend = and-the other addend.

Subtract the relationship between parts; Difference = minuend-minuend = minuend-difference = minuend+difference

The relationship between the parts of multiplication; One factor = product/another factor

The relationship between the parts of division; Quotient = dividend/divisor Divider = dividend/quotient dividend = quotient * divisor

The first volume of the fifth grade

The world of numbers

1. Numbers like 0, 1, 2, 3, 4, 5, 6 ... are natural numbers.

2. Things like -3, -2,-1, 0, 1, 2, 3, ... are integers.

Integers include natural numbers.

3. Multiples and factors: Multiples and factors are interdependent. For example: A×B=C, it can be said that A is a multiple of B and C, and B and C are factors of A, for example, 20 is a multiple of 4 and 5, and 4 and 5 are factors of 20. Note: We only study multiples and factors (except 0) within the range of natural numbers.

4. Odd and even numbers: numbers that are multiples of 2 are called even numbers, and numbers that are not multiples of 2 are called odd numbers.

5. Find a factor: find a factor of a number, one-on-one and orderly search, without repetition and omission. The smallest factor of a number is 1, and the largest factor is itself.

6. Multiply: from 1 time, search in order. A number has no maximum multiple. The smallest multiple is itself.

7. Prime number: A number has only two factors, 1 and itself. This number is called prime number.

8. Composite number: A number has other factors besides 1 and itself. This number is called a composite number. Note: 1 is neither a prime number nor a composite number.

9. According to the factor of a number, natural numbers can be divided into (prime number), (composite number) and (1 and 0). According to the parity of a number, natural numbers can be divided into two categories (odd and even). 0 is the smallest even number.

10. Supplement: Integer A is divisible by Integer B (B is not equal to 0), and the divisible quotient is exactly an integer without remainder, so we say that A can be divisible by B.

Multiplication characteristics of11.2,3,5: Numbers with 0,2,4,6,8 are multiples of 2. A number with 0 or 5 digits is a multiple of 5. The sum of each number is a multiple of 3, and this number is a multiple of 3.

12. prime factor: each composite number can be written as the product of several prime numbers. Every prime number is a factor of this composite number, which is called the prime factor of this composite number.

13. A composite number multiplied by a prime factor is called prime factor decomposition.

14. The common factor of several numbers is called the common factor of these numbers. The biggest one is called their greatest common divisor.

15. Two numbers whose common factor is only 1 are called prime numbers.

16. The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.

17. A fraction whose denominator is a prime number is called the simplest fraction.

18. approximation: it is called approximation to change a fraction into a fraction equal to it, but with smaller numerator and denominator.

Note: Try to calculate with your mouth when making an appointment. Generally, the common factor of the numerator denominator (except 1) is used to remove the numerator denominator of the fraction; Usually, we have to separate it until we get the simplest score.

19. Comprehensive score: the score of different denominators is changed into the score of the same denominator equal to the original score, which is called comprehensive score.

The general method of general division is: first find the least common multiple of the original denominator, and then divide the score into fractions with this least common multiple as the denominator.

20. Decimal decimal, there are several decimals, just write a few zeros after 1 as the denominator, and remove the decimal point after the original decimal point as the numerator; After the number of components, the number of quotation points can be reduced.

2 1. Fractional decimals with denominators other than integer 10, integer 100 or integer 1000 shall be denominated, and several decimals may be reserved according to rounding if necessary.

22. (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. )

23. The number of factors of a number is limited, and the number of multiples of a number is infinite. The minimum prime number is 2, the minimum composite number is 4, the minimum odd number is 1, odd number+odd number = even number+even number = even number-even number = even number, odd number+even number = odd number.

Summary of the concept of the first volume of sixth grade mathematics

First unit position

1. To find a location, you should first list the columns and then write out the rows. The format is: (column, row).

Unit 2 Overview of the Concept of Fractional Multiplication

1. Fractional multiplication of integers has the same meaning as integer multiplication, and it is a simple operation to find the sum of several identical addends.

For example, ×5 means a simple operation to find the sum of five consecutive additions.

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. In order to simplify the calculation, what can be reduced must be reduced first and then multiplied. )

Note: When multiplying with a fraction, the fraction should be converted into a false fraction before calculation.

3. A number multiplied by a fraction can be regarded as finding a fraction of this number.

For example, 5× means: What is the number of 5?

0.8× means: What is 0.8?

4. Calculation rules of fractional multiplication: fractional multiplication, the product of molecular multiplication is numerator, and the product of denominator multiplication is denominator. (In order to simplify the calculation, you can divide points first and then multiply them. )

Note: When multiplying with a fraction, the fraction should be converted into a false fraction before calculation.

5. The commutative law, associative law and distributive law of integer multiplication are also applicable to fractional multiplication.

6. Two numbers whose product is 1 are reciprocal.

7. To find the reciprocal of a number (except 0), just switch the numerator and denominator of this number.

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.

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

For example: 15×

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

For example: 25× = 25,14× >; 14 。

10. A number (except 0) times a fraction, and the product is greater than itself.

For example: 36× 2 >; 36 。

1 1. Fraction application problems are usually solved by digression.

(1) Find out the key sentences with scores.

(2) Find out the quantity of the unit "1" (hereinafter referred to as "standard quantity")

(3) Draw a line graph. Standard quantity and comparison quantity are the whole and part relationship. Just draw a line segment. Standard quantity and comparison quantity are not the whole and part relationship. Just draw two lines.

(4) Write the equivalence relation according to the line segment diagram: standard quantity × corresponding score = comparison quantity.

(5) According to the known conditions and problems.

13. The concept of attention in multiplication application problems.

(1) Ideas for solving multiplication application problems: Given a number, what is the score of this number?

(2) The method of finding the unit "1": find from the key sentences containing scores, and pay attention to the rules before "de" and after "bi".

(3) A score greater than B means a score greater than B, and a score less than B means a score less than B. ..

(4) Jiang rule: more than one thing is better than less, and less than one thing is better than more. For example, 8 is greater than 5 and 6 is less than 9. On the application issues, such as:

Last year, the rice yield per mu in Xiaohu Village was 750 kilograms. This year, rice yields 800 kilograms per mu. What is the increase? "Increasing production" in the title means more, so whoever is more than who should be "more than less", "more" means 800 kg, and "less" means 750 kg, which means that 800 kg is several times that of 750 kg. Combined with the expression of application questions, it can be added as "How many times is the yield per mu of rice this year more than last year?"

(5) Increase, improve and increase production. There are many meanings, while there are few meanings of reduction, decline and layoffs, which are similar to accounting, yes and equal.

(6) When the unit "1" in the key sentence is not obvious, it is necessary to complete the key sentence and add the form of "who is who" or "A is greater than B" or "A is less than B".

(7) In the multiplication problem, the unit "1" is known.

(8) The different fractions of "1"cannot be added or subtracted, which belongs to the phase difference ratio and always follows the law of "everything is consistent".

(9) The score should correspond to the quantity.

(1) The ratio of comparison quantity to comparison quantity; (2) the number of comparisons is small, and the score is small; (3) the ratio of the increased comparison amount to the increased score;

(4) the ratio of the reduced comparison amount to the reduced score;

⑤ Improved comparison quantity and improved score;

⑥ Reduced comparison quantity versus reduced score;

⑦ The ratio of the relative amount of the total workload to the total workload; (8) The ratio between the relative quantity of work efficiency and work efficiency;

Pet-name ruby part of the comparison of a part of the score; Attending the ratio of the comparative amount of the total amount to the total amount;

Unit 3 Summary of the Concept of Fractional Division

1. Meaning of fractional division: The meaning of fractional division is the same as that of integer division, and it is an operation to find the other factor by knowing the product of two factors and one of them.

For example:

Representation: What is the product of two numbers and one of the factors and the other factor?

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

3. Calculation rule of number divided by fraction: number divided by fraction equals the reciprocal of number multiplied by fraction.

4. 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. The quotient obtained by dividing the former term by the latter term is called the ratio. From the application point of view, the ratio can be divided into homogeneous ratio and heterogeneous ratio; The ratio of the same kind indicates the multiple relationship, and the front and back items of the ratio must be in the same unit; The results of different category ratios produce new quantities, and the units of the former and the latter are different.

6. Ratios are usually expressed in fractions, decimals and integers.

7. The last item of the ratio cannot be 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;

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.

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.

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

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

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

Unit 3 Overview of Elementary Fractional Arithmetic Concepts and Application Problems

1. The order of fractional elementary arithmetic is the same as that of integer elementary arithmetic. In the calculation with main operation and secondary operation, the secondary operation should be calculated first and then the main operation, that is, multiplication and division first and then addition and subtraction. In the operation at the same level, it should be calculated from left to right.

2. In fractional elementary arithmetic, arithmetic can be applied to make the calculation simple.

The algorithm includes: the commutative law of addition, the associative law of addition, the commutative law of multiplication, the associative law of multiplication and the distributive law of multiplication.

3. Matters needing attention in solving fractional application problems: the same as Unit 2.

Unit 4 Overview of the Concept of Circle

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

2. Fold a circular piece of paper twice, and the point where the crease intersects the center of the circle 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.

Expressed in letters: d = 2r or r = d/2.

9. Circumference: The length of the curve around a circle is called circumference.

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 pi, which is expressed by letters. Pi is an infinite cyclic decimal. In the calculation, π ≈ 3. 14 is taken. The first person in the world to calculate pi was China mathematician Zu Chongzhi.

1 1. The circumference formula 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. Cut a circle into an approximate rectangle. The length of the cut rectangle is equivalent to half of the circumference, and the width is equivalent to the radius of the circle. Because the area of a rectangle = length × width, and the area of a circle = π× r× r.

14. formula of circular area: s = π R2 or S= π()2 or S= π(C÷π÷2)2.

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

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

17. A ring, the radius of the outer circle is R, the radius of the inner circle is R, and its area is S = π R2-π R2.

Or s = π (R2-R2). (where r = the width of the ring. )

18. Ring circumference = outer circumference+inner circumference

19. The circumference of a semicircle is equal to half the circumference plus the diameter.

The perimeter formula of a semicircle: c = π d ÷ 2+d or c = π r+2r.

20. area of semicircle = area of circle ÷2 The formula is: s = π R2 ÷ 2.

2 1. How many times the radius of the same circle is enlarged or reduced, the diameter and circumference are also enlarged or reduced by the same times. And the area is expanded or reduced by the square of the multiple.

For example, the radius, diameter and circumference of the same circle are enlarged by four times, and the area is enlarged by 16 times.

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

For example, if the radius ratio of two circles is 2: 3, then the diameter ratio and perimeter ratio of these two circles are both 2: 3, while the area ratio is 4: 9.

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

When the diameter of a circle increases by one centimeter, the circumference increases by one centimeter.

24. 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.

25. 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.

26. Sector arc length formula: L = π d ÷ 360× n

Sector area formula: s s S= πr2÷360×n n n.

(n is the degree of the central angle of the sector, and r is the radius of the circle where the sector is located)

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

28. Only the figures of 1 axis of symmetry are: angle, isosceles triangle, isosceles trapezoid, sector and semicircle.

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

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

Figures with only four axes of symmetry are: squares;

……

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

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

Unit 5 Overview of Percent Concept

1. Definition of percentage: A number indicating that one number is a percentage of another number is called a percentage. Percentages are also called percentages or percentages.

Percent indicates the proportional relationship between two numbers, not the specific quantity, and there is no unit name.

2. Meaning of percentage: It means that one number is the percentage of another number.

For example, 25% means that one number is 25% of another.

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. Rules for decimal and percentage exchange:

To convert decimals into percentages, just move the decimal point two places to the right, followed by hundreds of semicolons;

To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.

5. Reciprocity rule of percentage and score:

When a fraction is converted into a percentage, it is generally converted into a decimal (except for three decimal places) and then converted into a percentage;

Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.

6. Percentage formula:

Qualified rate =× 100%

Germination rate =× 100%

Attendance rate =× 100%

……

7. Tax payment: Tax payment refers to paying a part of the collective or individual income to the state at a certain tax rate according to the relevant provisions of various national tax laws.

8. Significance of tax payment: tax payment is one of the main sources of national fiscal revenue. The state will use the tax collected for the development of economy, science and technology, education, culture and national defense security.

9. Tax types: Taxes are mainly divided into value-added tax, consumption tax, business tax and personal income tax.

10. Tax payable: The tax paid is called tax payable.

1 1. tax rate: the ratio of taxable amount to various incomes is called tax rate.

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

13. Significance of saving: People often deposit temporarily unused money in banks or credit cooperatives, which can not only support national construction, but also make personal use of money safer and more planned, and increase some income.

14. deposit types: deposits are divided into demand, lump-sum deposit and withdrawal, and lump-sum deposit and withdrawal.

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

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

17. According to national regulations, the tax rate of deposit interest is 5%. There is no tax in debt interest.

18. interest rate: the ratio of interest to principal is called interest rate.

19. Calculation formula of after-tax interest of bank deposits: after-tax interest = principal × interest rate × time × (1-5%)

20. Bank deposit interest tax = interest × 5% or bank deposit interest tax = principal × interest rate × time × 5%.

2 1. Calculation formula of debt interest: interest = principal × interest rate× time.

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

Mathematical concepts in the first semester of junior high school

The first chapter is a rich graphic world.

1. Prisms include straight prisms and oblique prisms.

2. Graphics are composed of points, lines and surfaces.

3. Faces intersect to get lines, and lines intersect to get points.

4. Point to line, opposite the line, facing the body.

5. In a prism, the intersection of any two adjacent faces is called an edge, and the intersection of two adjacent sides is called a side. All sides of a prism are equal in length. The upper and lower bottom surfaces of the prism have the same shape, and the side surfaces are rectangular.

6. Cut a cuboid with a plane, and the section is called a section.

7. Call it front view, left view and top view.

8. A plane figure is a closed figure composed of some line segments that are not on the same straight line.

9. A graph consisting of an arc and two radii passing through the end of the arc is called a fan.

Chapter II Rational Numbers and Their Operations

1. rational number: integer positive number, 0, negative number; Irrational number: positive and negative fractions.

2. Numbers greater than 0 are called positive numbers, which are represented by the symbol+(pronounced as positive numbers).

3. A number less than 0 is called a negative number, which is represented by the symbol-(pronounced negative).

4.0 is neither positive nor negative.

5. Draw a horizontal straight line, take a point on the straight line to represent 0 (called the origin), choose a certain length as the unit length, and specify the right direction on the straight line as the positive direction to get the number axis.

6. Any rational number can be represented by a point on the number axis.

7. If two numbers are only different in sign, then we call one of them the inverse of the other number, which is also called the inverse of each other. The antonym of 0 is 0.

8. The number represented by two points on the number axis is always larger on the right than on the left.

9. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.

10. The distance between the point corresponding to a number and the origin on the number axis is called the absolute value of the number.

1 1. The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.

12. Comparing two negative numbers, the larger absolute value is smaller.

13. Add two numbers with the same symbol, take the same symbol, and add the absolute values; Two numbers with different signs are added, and the sum is 0 when the absolute values are equal; When the absolute values are not equal, take the sign of the number with larger absolute value and subtract the number with smaller absolute value from the number with larger absolute value; Add a number to 0 and you still get the number.

14. Subtracting a number is equal to adding the reciprocal of this number.

15. When two numbers are multiplied, the sign of the same symbol is negative, and the absolute value is multiplied. Multiply any number by 0, and the product is still 0.

16. Two rational numbers whose product is 1 are reciprocal.

17. Divide two rational numbers, the same sign is positive and the different sign is negative, and divide by the absolute value. Divide 0 by any number except 0 to get 0. 0 cannot be partitioned.

18. Dividing by a number is equal to multiplying the reciprocal of this number.

19. the operation of finding the product of n identity factors a is called power, the result of power is called power, a is called base, and n is called exponent.

20. Calculate the power first, then multiply and divide, and finally add and subtract; If there are brackets, count them first.

Chapter III Letter Representation of Numbers

1. The formula of numbers or letters connected by operation symbols is called algebraic expression, and a single number or letter is also an algebraic expression.

2. Items with the same letter and the same letter index are called similar items. Merging similar items into one item is called merging similar items.

3. When merging similar items, we add up the coefficients of similar items, and the indexes of letters and letters remain unchanged.

There is a "+"before the bracket. After removing the brackets and the "+"sign in front of them, the symbols of the items in the original brackets remain unchanged; There is a "-"before the brackets. After removing the brackets and the "-"sign in front of them, the symbols of the original brackets will change.

Chapter IV Plane Figures and Their Positional Relations

The 1. line segment has two endpoints; Extending a line segment infinitely in one direction forms a ray, which has an endpoint; A straight line is formed by an infinite extension of a line segment in two directions, and the straight line has no end points.

There is a straight line after two o'clock.

3. In the connection between two points, the line segment is the shortest. The length of the line segment between two points is called the distance between these two points.

4. An angle is a graph composed of two rays with a common endpoint, and the common endpoint of the two rays is the vertex of the angle.

5. An angle can also be regarded as a ray rotating around its endpoint.

6. A ray drawn from the vertex of an angle divides the angle into two equal angles. This ray is called the bisector of the angle.

7. We usually use "∨" to indicate parallelism. After passing a point outside the straight line, there is one and only one straight line parallel to this straight line; If both lines are parallel to the third line, then the two lines are parallel to each other; Two straight lines intersect and there is only one intersection.

8. We usually use ⊥. In the plane, there is one and only one straight line perpendicular to the known straight line; Of all the line segments connecting the outer point and the point on the line, the vertical line segment is the shortest.

9. If two straight lines intersect at right angles, they are perpendicular to each other.

10. The intersection of two vertical lines is called vertical foot.

Chapter 5 One-variable linear equation

1. In an equation, there is only one unknown x (element), and the exponent of the unknown is 1 (degree). Such an equation is called a one-dimensional linear equation.

2. Adding (or subtracting) the same algebraic expression on both sides of the equation at the same time, the result is still an equation.

3. Both sides of the equation are multiplied by the same number at the same time (or divided by the same number that is not 0), and the result is still an equation.

Chapter VI Data in Life

1. Use circles and sectors to represent the relationship between the whole and the parts, that is, use circles to represent the whole, each sector in the circle represents different parts of the whole, and the size of the sectors reflects the percentage of the parts in the whole. This kind of statistical chart is called departmental statistical chart.

2. In the sector statistical chart, the percentage of each part in the whole is equal to the ratio of the central angle of the sector corresponding to this part to 360.

3. The pie chart can clearly show the percentage of each part in the total.

Bar chart can clearly show the specific figures of each project.

5. The broken line statistical chart can clearly reflect the changes of things.

Chapter VII Possibility

1. In life, there are some things that we can be sure will happen in advance. These things are called inevitable events. Some things we can make sure in advance will not happen. These things are called impossible events. Inevitable events and impossible events are certain.

There are still many things that we can't be sure whether it will happen in advance. This kind of thing is called uncertain events. The possibility of an uncertain event depends on its size. rational number

Give me the best answer.