Key points of primary school mathematics knowledge
I. Significance
1, which means: after sorting out the collected data, fill it in a table with a certain format for reverse.
Reflect the situation and explain the problem.
Statistical table 2. Category: (1) Single type.
(2) double entry.
1, which means: show the quantitative relationship in statistical data graphically, make it concrete and give it to people.
impressive
Statistical chart
(1) Bar chart: It is easy to see the number of various quantities: simplex and polymorphic.
2. Category: (2). Broken line statistical chart: can clearly show the increase and decrease of quantity: single type and compound type.
⑶ Sector statistical chart: It can clearly show the relationship between the quantity of each part and the total amount.
Second, quantity.
Network diagram of 1 and decimals:
Pure decimals and finite decimals
Decimal infinite acyclic decimal
Infinite Decimal Pure Cyclic Decimal with Decimal
Infinitely cyclic decimal
Mixed cyclic decimal
2. Integer:
Multiple common multiples Least common multiple: The multiple shared by several numbers is called the common multiple of these numbers.
Multiples, the smallest of which is called these numbers.
Least common multiple of divisibility.
The greatest common divisor of common divisor: The divisor of several numbers is called the common divisor of these numbers.
Factors, the largest of which are called these figures.
The greatest common divisor of.
Prime compound prime number
Prime factor decomposition prime factor
Characteristics of Numbers Divisible by 2.3.5
3. Prime number: concept: the common divisor has only 1 two numbers.
(1), some coprime (1), 1 and any natural number; ② Two adjacent natural numbers;
Prime number ③, two different prime numbers)
(2), not necessarily coprime (①, a prime number and a composite number; (2), two different composite numbers)
Prime number: If a number has only 1 and two divisors of itself, it is called a prime number.
Complex number: a number. If there are other divisors besides 1 and itself, it is called a complex number.
★ The divisor of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself; The number of multiples of a number is infinite, and the smallest multiple is itself. The minimum multiple of a number is equal to its maximum divisor.
★ When the integer A is divided by the integer b(b≠0), the quotient is exactly an integer without remainder, so we say that A can be divisible by b(b≠0) or b(b≠0) can be divisible by A ... This is the most basic concept in the divisible part of knowledge.
Natural numbers are divided into odd numbers and even numbers according to whether they can be divisible by 2.
Natural numbers are divided into 0, 1, prime numbers and composite numbers according to the divisor.
A natural number is divided by a divisor, and 0 has an infinite divisor, divided by all natural numbers (except 0).
rewrite
Rewrite the scores whose initials are 10, 100, 1000, ... and then lower the scores.
decimal
Divide the numerator by the denominator
Move the decimal point two places to the right, and then add%
Write in fractional form, subtract points.
If% is deleted, the decimal point will be written as a decimal first.
Move two places to the left. Then write it as a percentage.
per cent
In order to facilitate reading and writing, a large multi-digit number is often rewritten as a number with the unit of "10,000" or "100 million". Sometimes the mantissa after a certain digit of this number can be omitted and written as an approximation.
Step 4 compare
Fraction: Fraction with the same denominator, the fraction with larger numerator is larger; Fractions with the same numerator have larger scores with smaller denominator; The numerator and denominator are different, so compare the scores.
Integer comparison of numbers: look at the number in a bit first, the greater the number in a bit, the greater it will be; The number of digits is the same, and the number of digits is larger; Same number of digits, large number of digits. ...
Decimal: compare the sizes of two decimals, first look at their integer parts, the number with large integer part will be large, and the number with small integer part will be small; 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. ...
5. Numbers
Integer part decimal part decimal part
..... billion-level, 10,000-level personal level.
Digital ... billions of bits, billions of bits, billions of bits
10 million, 1 million, 100 thousand, 10 thousand
1,000 th place
Baiwei
West Usagur Ramgoolam Airport
a little
place
.
Ten percentage points, a thousand percentage points ...
Counting units ... thousands.
Baiyi
Billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion, billion. ...
Integers and decimals are numbers written in decimal notation, where 1, 10, 100,110,100 are counting units. The position occupied by each counting unit is called a digit. These figures are arranged in a certain order.
Numbers: when writing numbers, the units of calculation are arranged in a certain position in a certain order, and the positions occupied by different units of calculation are called numbers.
Number of digits: The number of digits in an integer is called the number of digits. A number containing a number is called a single digit.
6. Significance
Natural number: When we count objects, 1, 2, 3, ... are called natural numbers. There is no object, which is represented by 0. 0 is also a natural number. Natural numbers are all integers.
Fraction: divide the unit "1" into several parts on average, and the number representing such one or several parts is called a fraction. The number representing one of them is the decimal unit of this fraction.
When two integers are divided, their quotient can be expressed as a fraction. Namely: a ÷ b = a/b (b ≠ 0)
Decimal: Divide the integer "1" into 10, 100, 1000, ... a few tenths, a few percent, a few thousandths ... can be expressed in decimal. For example, 0. 1 is a decimal.
Finite decimal: the decimal part of a decimal has a limited number of digits, which is called a finite decimal.
Cyclic decimal: a decimal, starting from a certain bit of the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals. The number of digits in the decimal part is infinite, which is called infinite decimal. Cyclic decimal is infinite decimal.
Supplementary (1) four operations: in the formula without brackets, if there are operations of the same level, they should be calculated from left to right in turn; If there are two levels of operation, do the second level operation first, and then do the first level operation. If you are in a bracket formula, you have to calculate what is in brackets first, and then what is in brackets.
Note: when calculating, you should carefully examine the questions, see clearly the characteristics of operation symbols and numbers, and choose a reasonable calculation method flexibly.
Three. Four operations
(1) four operations
Digital range
Operational importance
Name, integer, decimal, fraction, letter
Addition (first-order operation) The operation of combining two numbers into one number. It means the same as integer addition. Same meaning as integer addition. A+B = C。
Subtraction (first-order operation) An operation in which the sum of two numbers is known, and one of them can be added to find the other. It has the same meaning as integer subtraction. It has the same meaning as integer subtraction. c-b=a
Multiplication (quadratic operation) is a simple operation to find the sum of several identical addends. Multiplying a number by a decimal can be regarded as finding a few tenths, a few percent ... Multiplying a number by a fraction can be regarded as finding a fraction of this number. a×b=c
Division (secondary operation) knows the product of two numbers and one of the factors, and the operation of finding the other factor has the same meaning as integer division. c÷b=a
Subtraction is the inverse operation of addition; Division is the inverse operation of multiplication; Multiplication is a simple operation of adding the same number; Division is a simple operation of subtraction with the same number.
There are four types: ①, ② at the same level, ③ at two levels, ④ with brackets, simple calculation.
(2) Algorithm and simple algorithm
Additive commutative law: A+B = B+A additive commutative law: A+B+C = A+(B+C)
A fast algorithm for addition and subtraction: A-B = A-C-D, A+B = A+C+D.
The nature of subtraction: a-b-c = a-(b+c) multiplicative commutative law: a× b = b× a.
Multiplicative associative law: a× b× c = a× (b× c) Multiplicative distributive law: (a+b )× c = a× c+b× c.
Property of product invariance: AB = (a× c )× (b× c) Property of division: A ÷ b ÷ c = A ÷ (b× c)
Invariance of quotient: A ÷ b = (A ÷ c) ÷ (B ÷ c), A ÷ b = (A× c) ÷ (B× c).
Fourth, the equation
Equation: An equation containing an unknown number is called an equation.
Algebra: 1 Using letters to represent numbers can concisely express quantitative relations, operation rules and calculation formulas.
2. Multiply the number with the letter, omit the multiplication sign and write the number before the letter. (e.g. 1a=a× 1)
3. When letters are multiplied by letters, the multiplication sign can be omitted, or it can be written as the abbreviation of the multiplication sign (for example, a× b = ab = a.b).
4. Numbers and numbers can't omit multiplication sign.
The value of the number of knowledge that makes the left and right sides of the equation equal is called the solution of the equation. Just a number.
The process of solving an equation is called solving an equation. Just a process.
When n stands for any natural number, 2n stands for even number, because it can be divisible by 2. 2n+ 1 stands for odd number.
Equation is not proportion, proportion is equation.
Verb (abbreviation of verb) application problem
1, simple application problem
The basic application problems in primary school mathematics are simple application problems, and various application problems are synthesized on the basis of simple application problems.
2. Composite application problems
Steps to solve general application problems (as follows)
(1) understanding the meaning of the question (basic) (2) analyzing the quantitative relationship (key) (3) formula calculation (key)
(4) Checking calculation (correctly grasping) (5) Writing sentences (complete and necessary)
Simple application problems can be divided into four categories: 1, and the relationship between total number and partial number. 2. The relationship between large numbers, decimals and differences. 3. Multiple, the relationship between multiple and multiple. 4, the total number of copies, the number of copies and the relationship between each copy. 1 1 species: (1) Sum. (2) seeking surplus. (3) Find the sum of the same numbers. (4) Average segmentation. 5] Including except. [6] The difference between two numbers. (7) How much is a large number more than a decimal? (8) How much is the decimal less than the large number? One number is several times that of another. ⑽ Find the multiple of a number. ⑾ If you know the fraction of one number and another, find this number.
Sixth, the relationship between ratio, fraction and division
The preceding paragraph-numerator-dividend proportion-fractional line-division number
The latter term-denominator-divisor ratio-fractional value-quotient
A ratio is a multiple relationship between two numbers. The score is a number. Division is an action.
VII. Proportion, Proportion
The division of two numbers is also called the ratio of two numbers, and the formula of two equal proportions is called proportion.
The basic nature of the ratio: the first and last items of the ratio are multiplied or divided by the same number (except 0), and the ratio remains unchanged.
The basic property of proportion: in proportion, the product of two internal terms is equal to the product of two external terms.
The difference between seeking ratio and simplifying ratio: seeking ratio is a quotient; The simplified ratio is a ratio, and the front and back terms are integers.
Proportional ratio: two related quantities, one change and the other change. If the ratio (that is, quotient) of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. Y/x = k (ok)
Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. X× y = k (sure)
Similarity of positive and negative proportions: there are three quantities, two of which are related quantities and one is definite quantity. As one quantity changes, the other quantity changes.
Eight, the difference between equation solution and arithmetic solution
The solution of the equation is positive thinking, and the amount of knowledge is the amount of knowledge. Arithmetic solution is reverse thinking.
1, fractional application problem
Comparison quantity/standard quantity =? /? Or? % (search percentage)
Number of "1" × corresponding score of required quantity = required quantity.
Equation solution: known quantity ÷ corresponding score = "1"
Nine, geometric figures
1, graphic area calculation formula table
Name area letter calculation formula area calculation formula
Length of rectangle s = area of rectangle ab = length × width
Square s positive = A2 square area = side length × side length
Triangle s triangle = ah ÷2 triangle area = bottom × height ÷2
Parallelogram s parallel = BH parallelogram area = base × height
Trapezoidal S ladder = (a+b) × h ÷2 Trapezoidal area = (upper bottom+lower bottom) × height ÷2.
Circle s circle = π R2 circle area = radius 2×π.
Sector (semicircle) s circle = π R2× n/360 Sector area = radius 2× pi× n/360
2, graphic perimeter calculation formula table
Name perimeter letter calculation formula perimeter calculation formula
Length of rectangle C = (a+b) ×2 Perimeter of rectangle = (length+width) ×2.
Square c is positive = 4a Square perimeter = side length ×4
triangle
Parallelism of parallelogram C = (a+b) ×2 Parallelism perimeter = (hypotenuse+base) ×2
trapeziform
Circle C Circle = 2π r Perimeter = Diameter× π.
Sector (semicircle) C Sector = dπ× n/360+2r Sector perimeter = diameter× pi× n/360+radius× 2
3. Driving speed
① Length unit:
1km =1000m1km =10000 decimeter1km =100000 cm1km =100000.
1 decimeter = 100 mm 1 cm = 10 mm.
② Area unit
1 square kilometer = 100 hectare = 1000000 square meter = 10000000 square decimeter = 1000000 square centimeter.
1 hectare = 10000 square meters = 1000000 square decimeter = 1000000 square centimeters.
1 m2 = 100 square decimeter = 10000 square centimeter 1 square decimeter = 100 square centimeter.
③ Volume (volume) unit
1 m3 = 1000 cubic decimeter = 1000 liter = 1000000 cubic centimeter = 1000000 ml.
1 cubic decimeter = 1 liter = 1000 cubic centimeter = 1000 ml 1 cubic centimeter = 1 ml.
④ Mass unit
1t = 1000kg = 100000g 1k g = 1000g。
⑤ Time unit
1 century = 100 1 year = 1 February =52 weeks =365 or 366 days a year = four seasons1season = 3 months.
1 month = 30 days (morning till night) 1 week =7 days 1 day =24 hours 1 hour =60 minutes 1 minute =60 seconds.
12 months, there are 7 big months and 4 small months, 1 small month. The big months are 1, 3, 5, 7, 8, 10, 65438+February; Abortion was in April, June and September, 165438+ 10; The moon is February. There are 29 days in February of leap year and 28 days in February of normal year.
4. Name and number
Nominal number: the measurement results should be expressed in numbers with the name of the unit, which are usually called nominal numbers together. For example:
count
5 meters singular 3 meters plural 3 points
Organization name
Rewriting names: In practice, names with the same number but different units often need to be rewritten. Rewrite the name of a high-level unit into the name of a low-level unit, multiply it by the propulsion rate, rewrite the name of a low-level unit into the name of a high-level unit, and divide it by the propulsion rate. When rewriting a name, for the sake of simplicity, we can apply the law that moving the decimal point causes the size of the number to change.
5. Angle
Straight line; A straight line is infinite.
Line segment: A segment between two points on a straight line is called a line segment. A line segment has two endpoints. A line segment is a part of a straight line.
Ray: Extend one end of a line infinitely, and you get a ray. A ray has only one endpoint.
Angle: The figure formed by two rays from a point is called an angle. This point is called the vertex of the angle. These two rays are called the edges of the angle. The angle is usually represented by the symbol "∞". As shown in the figure below:
edge
pinnacle
edge
Compare the sizes of angles: first overlap the vertices of two angles on one side, and then look at the position of the other side. Which corner has the other side outside, which corner is big. If the other side also coincides, the two angles are equal.
The size of the angle depends on the size of both sides. The bigger the fork, the bigger the angle. The size of the angle has nothing to do with the length drawn on both sides of the angle.
Measurement of angle: the unit of measurement of angle is "degree", which is represented by the symbol "0". Divide the semicircle into 180 equal parts, and the angle of each part is called 1 degree angle. Write 1. When measuring an angle with a protractor, place the protractor above the angle so that the center of the protractor coincides with the vertex of the angle. The 0 degree line coincides with one side of the angle, and the scale on the protractor on the other side of the angle is the degree of this angle.
Classification of angles: angles greater than 0 and less than 90 are called acute angles. An angle equal to 90 degrees is called a right angle. An angle greater than 90 and less than180 is called an obtuse angle. The two sides of an angle form a straight line, and the angle equal to 180 is called a right angle. The 360-degree angle formed by light rotating around its endpoint is called fillet.
Vertical line: When two lines intersect at right angles, they are called perpendicular to each other, one of which is called the vertical line of the other (as shown in the following figure 1), and the intersection of these two lines is called vertical foot.
Parallelism: Two straight lines that never intersect in the same plane are called parallel lines (Figure 2 below). It can also be said that these two straight lines are parallel to each other.
Vertical parallelism
6, rectangle, square
Both a rectangle and a square have four sides. Two sides of a rectangle are equal in length, and four sides of a square are equal in length. They all have four right angles. A square is a special rectangle.
7. Triangle
Classification of triangles: triangles with three acute angles are called acute triangles; A triangle with a right angle is called a right triangle; A triangle with an obtuse angle is called an obtuse triangle.
A triangle with two equal sides is called an isosceles triangle. In an isosceles triangle, two equal sides are called waist and the other side is called bottom; The included angle between the two waists is called the vertex angle; The two corners on the bottom edge are called bottom corners.
A triangle with three equilateral sides is called an equilateral triangle, also called a regular triangle. Draw a vertical line from the vertex of a triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle, and the opposite side is called the bottom of the triangle. The sum of the internal angles of a triangle is 180. Two identical triangles can be combined into a parallelogram.
8. Parallelogram
Two groups of parallelograms with parallel opposite sides are called parallelograms. None of the four corners are right angles.
Draw a vertical line from one point on one side of the parallelogram to the other. The line segment between this point and the vertical foot is called the height of the parallelogram, and the opposite side is called the bottom of the parallelogram.
Rectangular and square are special parallelograms.
8, trapezoidal
A quadrilateral with only one set of parallel sides is called a trapezoid.
In a trapezoid, a group of mutually parallel opposite sides are called the bottom of the trapezoid (usually the shorter bottom is called the upper bottom and the longer bottom is called the lower bottom); A group of non-parallel opposite sides is called trapezoidal waist; Draw a vertical line from a point on the upper bottom to the lower bottom, and the line segment between this point and the vertical foot is called the height of the trapezoid.
An isosceles trapezoid is called an isosceles trapezoid.
9. circle
The point of the center of the circle is called the center of the circle. The center of the circle is generally represented by the letter "O".
The line segment connecting any point on the center of the circle is called radius. Radius is usually represented by the letter "r".
The line segments passing through the center of the circle and the two ends of the circle are called diameters. The diameter is usually indicated by the letter "D".
A circle has countless radii and diameters. All diameters and radii are equal. The diameter is twice the radius. The radius is 1/2 of the diameter. The center of the circle determines the position of the circle, and the radius determines the size of the circle.
The ratio of the circumference to the diameter of a circle is called pi, which is expressed by the letter "π".
π=3. 14 1592653……
≈3. 14
10, sector, semicircle
The distance between any two points on the circumference is called an arc.
A figure surrounded by an arc and two radii passing through both ends of the arc is called a fan.
The angle between the two radii of the center of a circle. Like this, the angle of the vertex at the center of the circle is called the central angle. In the same circle, the size of the sector is related to the central angle of the sector.
1 1, axisymmetric graph
If a graph is folded in half along a straight line, the graphs on both sides can completely overlap. This graph is called an axisymmetric graph. The straight line where the crease lies is called the symmetry axis.
12, cuboid, cube
An edge where two faces intersect is called an edge. The point where three sides intersect is called a vertex.
A cuboid is a three-dimensional figure surrounded by six rectangles (in special cases, two opposite faces are squares). In a cuboid, the opposite faces are exactly the same, and the opposite sides are equal in length. A cuboid has 12 sides and 8 vertices. The length of three sides intersecting at a vertex is called the length, width and height of a cuboid.
A cube is a three-dimensional figure surrounded by six identical squares. A cube also has 12 sides, and their lengths are equal. A cube also has eight vertices.
Cubes and cuboids have the same number of faces, edges and vertices. Just the length of the cube. A cube can be said to be a cuboid with equal length, width and height. It is a special cuboid.
13, cylinder
The upper and lower surfaces of a cylinder are called the bottom surface. They are exactly the same two circles. Cylinders have countless heights. A cylinder has a surface called a side. The distance between the two bottom surfaces of a cylinder is called height, also called length, width and depth. Cutting off the edge of a vertical line will make it a rectangle, or you will get a square.
14, conical
The bottom of the cone is round, and the side of the cone is curved. The distance from the apex of the cone to the center of the bottom surface is the height h of the cone. A cone has only one base, and a cone has a vertex and a height. The side of the cone is fanned out.
Volume calculation formula
Name volume letter formula volume formula
Cuboid v cuboid = a× b× h cuboid volume = length× width× height
Cuboid v cuboid = a3 cuboid volume = side length × side length× side length
Cylinder v cylinder = π R2× h cylinder volume = pi × radius 2× height
Cone V Cone = 1/3 π R2× h Cone volume = pi× radius 2× height×1/3
Surface area calculation formula
Name surface area letter formula surface area formula
Cuboid s cuboid = (a× b+a× h+b× h )× 2 cuboid surface area = (length× width+length× height+width× height )× 2.
Cube of cube s = a× a× 6 Cube surface area = side length× side length× 6.
Cylinder s cylinder = π R2× 2+π d× h cylinder surface area = pi × radius 2× 2+ diameter× π× height.
Volume of cone = 1/3 bottom× product height. Formula: V= 1/3Sh
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) lateral 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%)