1. Little knowledge of fifth grade mathematics

Little knowledge of fifth grade mathematics 1. Knowledge points of mathematics of fifth grade in primary school

Knowledge points of final review of the first volume of primary school mathematics Induction of the first unit of decimal multiplication 1, decimal multiplication by integers (P2, 3): Meaning - a simple operation to find the sum of several identical addends.

For example: 1.5*3 means how much is 3 times 1.5 or a simple calculation of the sum of three 1.5s. Calculation method: first expand the decimal into an integer; calculate the product according to the rules of integer multiplication; then look at how many decimals there are in the factor, and count the number of decimal points from the right side of the product.

2. Multiply decimals by decimals (P4, 5): The meaning is to find out what fraction of this number is. For example: 1.5*0.8 is to find what eight tenths of 1.5 is.

1.5*1.8 is to find what is 1.8 times 1.5. Calculation method: first expand the decimal into an integer; calculate the product according to the rules of integer multiplication; then look at how many decimals there are in the factor, and count the number of decimal points from the right side of the product.

Note: In the calculation results, the 0 at the end of the decimal part should be removed to simplify the decimal; when there are not enough digits in the decimal part, 0 should be used as a placeholder. 3. Rule (1) (P9): When a number (except 0) is multiplied by a number greater than 1, the product is greater than the original number; when a number (except 0) is multiplied by a number less than 1, the product is smaller than the original number.

4. There are generally three methods for finding approximate numbers: (P10) ⑴ rounding method; ⑵ rounding method; ⑶ tailing method 5. When calculating the amount of money, keep two decimal places, which means the calculation is to cents. Round to one decimal place to indicate the angle.

6. (P11) The order of the four arithmetic operations on decimals is the same as that on integers. 7. Laws and properties of operations: addition: commutative law of addition: a+b=b+a associative law of addition: (a+b)+c=a+(b+c) subtraction: properties of subtraction: a-b-c=a-(b+ c) a-(b-c)=a-b+c Multiplication: Commutative law of multiplication: a*b=b*a Associative law of multiplication: (a*b)*c=a*(b*c) Distributive law of multiplication: ( a+b)*c=a*c+b*c (a-b)*c=a*c-b*c Division: Properties of division: a÷b÷c=a÷(b*c) Unit 2 Decimal Division 8. The meaning of decimal division: knowing the product of two factors and one of the factors, find the operation of the other factor.

For example: 0.6÷0.3 means that given the product of two factors 0.6 and one of the factors 0.3, find the operation of the other factor. 9. Calculation method of dividing decimals by integers (P16): Divide decimals by integers and divide them by integer division.

The decimal point of the quotient should be aligned with the decimal point of the dividend. If the integer part is not enough to divide, the quotient is 0 and put the decimal point.

If there is a remainder, add 0 and divide. 10. (P21) Calculation method of division when the divisor is a decimal: first expand the divisor and dividend by the same multiple so that the divisor becomes an integer, and then calculate according to the rule of "division by decimals when the divisor is an integer".

Note: If the number of digits in the dividend is not enough, add 0 at the end of the dividend. 11. (P23) In practical applications, the quotient obtained by decimal division can also use the "rounding" method to retain a certain number of decimal places as needed to find the approximate number of the quotient.

12. (P24, 25) Change rules in division: ① Invariant quotient property: If the dividend and divisor expand or contract at the same time by the same multiple (except 0), the quotient remains unchanged. ②The divisor remains unchanged, the dividend expands, and the quotient expands accordingly.

③The dividend remains unchanged, the divisor shrinks and the quotient expands. 13. (P28) Repeating decimals: In the decimal part of a number, starting from a certain digit, one number or several numbers appear repeatedly in sequence. Such decimals are called recurring decimals.

Cyclic section: The decimal part of a recurring decimal, numbers that appear repeatedly in sequence. For example, the cyclic section of 6.3232... is 32.14, and the number of digits in the decimal part is a finite decimal, which is called a finite decimal.

A decimal that has infinite digits in the decimal part is called an infinite decimal. Unit 3 Observing Objects 15. When observing objects from different angles, the shapes seen may be different; when observing a cuboid or cube, up to three faces can be seen from a fixed position.

Unit 4 Simple Equations 16. (P45) In equations containing letters, the multiplication sign between the letters can be recorded as "?", or it can be omitted. The plus sign, minus sign, division sign, and multiplication sign between numbers cannot be omitted.

17. a*a can be written as a?a or a, and a is read as the square of a. 2a means a+a18. Equation: An equation containing unknown numbers is called an equation.

The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. The process of finding the solution to an equation is called solving the equation.

19. Principle of solving equations: balance on the scale. If the same number (except 0) is added, subtracted, multiplied, and divided simultaneously on both sides of the equation, the equation still holds.

20. 10 quantitative relational expressions: addition: sum = addend + addend one addend = sum - two one addend subtraction: difference = minuend - minuend minuend = difference + Minus Minus = Minuend - Difference Multiplication: Product = Factor * Factor One factor = Product ÷ Another factor Division: Quotient = dividend ÷ Divisor Divisor = Quotient * Divisor Divisor = dividend ÷ Quotient 21. All equations are Equations, but equations are not necessarily all equations. 22. The process of testing the equation: the left side of the equation =... 23. The solution of the equation is a number; =... Solving the equation is a calculation process.

= Right side of the equation So, X=… is the solution to the equation. Unit 5 Area of ??Polygon 23. Formula: Rectangle: Perimeter = (Length + Width) * 2 - Length = Perimeter ÷ 2 - Width; Width = Perimeter ÷ 2 - Long Letter formula: C = (a + b )*2 Area = length * width Letter formula: S = a Square: Perimeter = side length * 4 Letter formula: C = 4a Area = side length * side length Letter formula: S = a Parallelogram area = base * height Letter formula: S=ah Area of ??triangle = base * height ÷ 2 - Base = area * 2 ÷ height; height = area * 2 ÷ base Letter formula: S = ah ÷ 2 Area of ??trapezoid = (upper base + lower base )*Height÷2 Letter formula: S=(a+b)h÷2——Upper bottom=Area*2÷Height-Lower bottom, Lower bottom=Area*2÷Height-Upper bottom; Height=Area*2÷ (Upper base + lower base) 24. Derivation of the formula for the area of ??a parallelogram: shearing, translation 25. Derivation of the formula for the area of ??a triangle: a rotated parallelogram can be converted into a rectangle; two identical triangles can be put together to form a parallelogram, a rectangle The length is equal to the base of the parallelogram; the base of the parallelogram is equal to the base of the triangle; the width of the rectangle is equal to the height of the parallelogram; the height of the parallelogram is equal to the height of the triangle; the area of ??the rectangle is equal to the area of ??the parallelogram, and the The area is equal to twice the area of ??the triangle, because the area of ??the rectangle = length * width, so the area of ??the parallelogram = base * height.

Because the area of ??the parallelogram = base * height, the area of ??the triangle = base * height ÷ 226. Derivation of the trapezoid area formula: rotation 27. The second derivation of triangles and trapezoids.

2. Mathematical knowledge for grade 5

A math joke 1. Once, my mother patiently inspired Yaya to do arithmetic problems: "Yaya, you have learned to do subtraction. Come on, let’s see, what’s 4 minus 2?”

“That’s right, good boy, what’s 5 minus 5?” 5 minus 5, minus 5." Yaya mumbled, "I can't do it, mom."

"Child, you can't do that!" There were 5 coins in your pocket, but suddenly, all 5 coins fell out. What else was in your pocket?" Yaya flashed her big eyes and said, "What about my pocket? There is a hole in it!" 2. "I always get 100 in the arithmetic test." "That's because you studied well." "But I never listen in class."

"That's because you are smart, and you know how to study hard when you get home from school." "Are you smart? A little bit, but after school, I am a person who deals with football."

"Then when you take the exam, you must "It's cheating." "You can't say that. I didn't write a note or peek at someone else's book. How can I cheat?" "Then how did you do it?" Kick the nerd Jim’s chair in front of me.” “No, no, how could you be so naughty?”

“I kicked him the first time, and he stretched out five fingers with his hand.” What does it mean?" "The answer to the first question is 2+3."

"Oh... what if the answer to the tenth question is 5*8?" "That's after I kicked the tenth ball. After that, he first stretched out four fingers, and then immediately clenched his fist, so I knew the answer to 40." 3. The teacher announced the results: "Xiao Hua has thirty points, Xiao Ming has twenty points..." Xiaozhu: Me. Got 0 points on the test! Puppy: What should I do? Me too... Piggy: We both got the same score in the exam. Will the teacher think we are cheating? 2 Mathematics Story It is said that one day, Zhuge Liang called his soldiers together and said: "Anyone among you, choose an integer from 1 to 1024 and keep it in your mind. I will ask ten questions and only ask for a 'yes' answer." Or 'no'.

After answering all ten questions, I will 'calculate' the number in your mind." Just as Zhuge Liang finished speaking, a counselor stood up and said that he had made his choice. A number.

Zhuge Liang asked: "The number you chose is greater than 512?" The counselor replied: "No." Zhuge Liang asked the counselor nine more questions, and the counselor answered them one by one.

Zhuge Liang finally said: "The number you remembered is 1." The counselor was extremely surprised when he heard this, because this number was really the number he chose.

Do you know what Zhuge Liang did? In fact, the method is very simple, that is, take half and half of 1024. When the tenth time is taken, it is "1". According to this principle, you can find the required number by asking ten questions in a row.

3. Mathematics Quotes 1. Wang Juzhen’s Percentage Chinese scientist Wang Juzhen has a motto when it comes to experimental failures, which is: “If you keep doing it, there is a 50% chance of success. If you don’t do it, it will be a 100% failure.” 2 , Tolstoy's score When the great Russian writer Tolstoy talked about the evaluation of people, he compared people to a score.

He said: "A person is like a fraction. His actual talent is like the numerator, and his valuation of himself is like the denominator. The larger the denominator, the smaller the value of the fraction."

1. The essence of mathematics lies in its freedom. Cantor 2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. Cantor 3. None Any question can touch people's emotions as deeply as infinity. Few other concepts can stimulate the intellect to produce more fruitful thoughts. Yet no other concept needs as much elucidation as infinity. Silber Hilbert 4. Mathematics is an infinite science. Hermann Weyl 5. Questions are the heart of mathematics. P.R. Halmos 6. As long as a branch of science can raise a large number of questions, it is full of vitality, while the lack of questions will It heralds the termination or decline of independent development. Hilbert 7. Some beautiful theorems in mathematics have the following characteristics: they are easily summarized from the facts, but the proofs are extremely hidden. Gauss 3. Rybakov’s constant and Variables Russian historian Rybakov said this about the use of time: "Time is a constant, but for diligent people, it is a 'variable'. People who use 'minutes' to calculate time are more likely to use 'hours' to calculate time. People who count time have 59 times more time. ”

2. Use symbols to write mottos 4. Hua Luogeng’s minus sign Hua Luogeng, a famous Chinese mathematician, pointed out when talking about learning and exploration: “You must dare to do it in learning. Subtraction is to subtract the parts that have been solved by predecessors to see what problems remain that need to be explored and solved.” 5. Edison’s Plus Sign The great inventor Edison used a plus sign to describe genius when he talked about it. Said: "Genius = 1% inspiration + 99% blood and sweat."

6. Dimitrov's plus and minus sign Dimitrov, the famous international workers' movement activist, evaluated the day's events When working, he said: "Use your time to think about what you did during the day, whether it is a 'plus' or a 'minus'. If it is '+', you have made progress; if it is '-', you have to learn a lesson. Take measures." 3. Aphorisms written with formulas 7. Einstein's formula When Einstein, the greatest scientist in modern times, was talking about the secret of success, he wrote down a formula: A=x+y+z.

And explained: A represents success, x represents hard work, y represents the correct method, and Z represents less empty words. ""If the small circle represents the knowledge you have learned, and the large circle represents the knowledge I have learned, then the area of ??the large circle is a little larger, but the blank space outside the two circles is our ignorance.

The larger the circle, the more ignorant surfaces its circumference touches. ” - Zeno Cauchy (A. L. Cauchy, 1789 – 1857) Men pass away, but their deeds abide. Men always die, but their deeds endure forever.

Laplace (1749) – 1827) What we know is not much. What we do not know is immense. C. Hermice 1822 – 1901 Abel has left mathematicians. enough to keep them busy for 500 years. When he evaluated Abel, he once said: "What Abel left behind can keep mathematicians busy for 500 years."

Poisson, Siméon 1781-1840) "Life is good for only two things, discovering mathematics and teaching.

3. Summary of key mathematical knowledge for the first to fifth grade of primary school (detailed)

All for the fifth grade of primary school Summary of subject courseware lesson plan exercises for the third unit of Chinese Mathematics. There are two opposite faces of a square, and the opposite faces of the cuboid are exactly the same; there are 12 edges, and the lengths of the opposite edges are equal; and there are 8 vertices.

2. , Characteristics of a cube: The cube has 6 faces, all of which are squares, and all faces are exactly the same; it has 12 edges, all of which are equal in length; and it has 8 vertices. The cube can be regarded as length, width, and length. A cuboid with equal heights.

3. The lengths of the three edges that intersect at a vertex are called the length, width, and height of the cuboid. 4. The total length of the 12 edges of the cuboid or cube is called their length. The sum of the edge lengths.

The sum of the edge lengths of a cuboid = (length + width + height) * 4, which can be expressed in letters as = C? cuboid (a + b + h) 4. The sum of the edge lengths of a cube = edge length * 12, which can be expressed in letters as = 12aC cube.

5. The total area of ??the six faces of a cuboid or cube is called its surface area. The surface area of ??a cuboid = (length * width + length * height + width * height) * 2, expressed in letters as = (ab + ah + bh) 2S? cuboid.

The surface area of ??the cube = edge length * edge length * 6, expressed in letters as 2 = 6aS cube. 6. The size of the space occupied by an object is called the volume of the object.

To measure volume, volume units must be used. Commonly used volume units include cubic centimeters, cubic decimeters, and cubic meters, which are expressed in letters as 3cm, 3dm, and 3m. 3311000dmcm?, 3311000mdm?.

7. A cube with an edge length of 1 cm has a volume of 13cm. The volume of a fingertip is approximately 13cm.

A cube with edge length 1 dm has a volume of 13 dm. The volume of a chalk box is approximately 13cm.

A cube with edge length 1 m has a volume of 13m. Use three 1 m long wooden strips to make a shelf at right angles to each other and put it in the corner. Its volume is 13cm.

8. The volume of a cuboid = length * width * height, expressed in letters as = abhV cuboid. The volume of the cube = edge length * edge length * edge length, expressed in letters as 3 = aV cube.

The unified formula of cuboid and cube: volume of pillar = base area * height. 9. The volume of an object that a container can hold is called its volume.

To measure volume, volume units are generally used to measure the volume of liquids. Commonly used volume units are liters and milliliters, represented by letters L and ml. 4 311Ldm?, 311mlcm?, 11000Lml? 10. The calculation method of the volume of a rectangular or cube container is the same as the calculation method of the volume.

But measure the length, width, and height from inside the container. 11. To find the volume of irregularly shaped objects, you can use the drainage method.

The volume of the part of the water that rises or falls is the volume of the object. Unit 4 1. The meaning of fractions 1. When measuring, dividing objects or calculating, it is often not possible to obtain an exact integer result. In this case, fractions are often expressed.

2. An object, some objects, etc. can be regarded as a whole. The whole can be divided into several parts. Such one or several parts can be expressed as fractions. Divide something equally and that is the unit "1".

3. Divide the unit "1" evenly into several parts, and the number representing one part is called a fractional unit. The larger the denominator of a fraction, the smaller the unit of the fraction; the smaller the denominator of a fraction, the larger the unit of the fraction.

4. The relationship between fractions and division: Fractions can represent the quotient of integer division; the dividend in division is equivalent to the numerator in the fraction, the divisor is equivalent to the denominator in the fraction, and the sign is equivalent to the fraction line. =? dividend dividend dividend divisor divisor, =? numerator numerator denominator denominator.

5. How to solve the problem of finding what fraction of one number is another number: use division calculation. =?One number, one number, another number, and another number. When solving problems, you must first find the unit "1" and the comparison quantity. Generally speaking, the unit "1" is followed by "is" or "account" in the problem. , if these two words do not appear in the previous comparative quantity, you must judge according to the meaning of the question, and then calculate according to the formula "1=1? Comparative quantity Comparative quantity unit "" unit "" ".

6. When a low-level unit is transformed into a high-level unit (expressed as a fraction), it is equal to the value of the low-level unit. The rate of progression between the two units can be reduced to the simplest fraction. 2. Proper fractions and improper fractions 1. A fraction whose numerator is smaller than its denominator is called a proper fraction, and a proper fraction is less than 1; a fraction whose numerator is larger than its denominator or whose numerator and denominator are equal is called an improper fraction, and an improper fraction is greater than or equal to 1; from the integer part (excluding 0) and a proper fraction are called mixed numbers.

2. To convert an improper fraction into an integer or a mixed number, divide the numerator by the denominator. When the numerator is a multiple of the denominator, 5 can be converted into an integer; when the numerator is not a multiple of the denominator, it can be converted into a mixed number. The quotient is the integer part of the mixed number, and the remainder is the numerator of the fraction part, and the denominator remains unchanged.

3. To convert a mixed number into an improper fraction, use the original denominator as the denominator, use the product of the denominator and the integer plus the original numerator as the numerator, and use the formula to express: +=? denominator integer numerator band Fraction denominator 3. Basic properties of fractions, reduction fractions, common fractions 1. Basic properties of fractions: The numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged. You can use the basic properties of fractions to reduce or divide fractions, or convert the denominator into a fraction with a specified denominator or numerator.

2. The factors that two numbers have in common are called their common factors. The greatest common factor among them is called their greatest common factor.

When two numbers are multiples, the smaller number is their greatest common factor; when two numbers only have a common factor of 1, their greatest common factor is 1. (The common factor is only 1 Two numbers are called coprime numbers) 3. To find the greatest common factor of two numbers, you can use the enumeration method to list the factors of the two numbers respectively, and then find the common factors. It can also be calculated using short division.

4. A fraction whose numerator and denominator only have a common factor of 1 is called the simplest fraction. Converting a fraction into a fraction that is equal to it but has smaller numerator and denominator is called a reduction.

When reducing, you can use the common factors of the numerator and denominator (except 1) to divide, step by step, or you can directly use the greatest common factor to divide directly. 5. The common multiples of two numbers are called their common multiples, and the smallest multiple is called their least common multiple.

In general, to find multiples of a number, you can use the enumeration method, the graphic method, the doubling method of large numbers, and the short division method. When two numbers are multiples, the large number is their least common multiple; the least common multiple of two relatively prime numbers is their product.

6. Convert the fractions with different denominators into the same fractions that are equal to the original fractions.

4. Review of mathematical concepts and knowledge points for grades one to five of primary school

Basic formula: 1 Number of copies * number of copies = total number of total number ÷ number of copies = total number of copies ÷ number of copies = Number of copies per copy 2 1 multiple * multiple = how many multiples how many multiples ÷ 1 multiples = how many multiples ÷ multiples = 1 multiples 3 speed * time = distance distance ÷ speed = time distance ÷ time = speed 4 unit price * quantity = total price total price ÷Unit price = Total price of quantity ÷Quantity = Unit price 5 Work efficiency * Working time = Total amount of work Total amount of work ÷ Work efficiency = Total working time ÷ Total working time = Work efficiency 6 Addend + Addend = sum and - one plus Number = another addend 7 Minuend - Minuend = Difference Minuend - Difference = Minuend Difference + Minuend = Minuend 8 Factor * Factor = Product ÷ One factor = Another factor 9 Divisor ÷ Divisor = Quotient and dividend ÷ quotient = divisor quotient * divisor = dividend Primary school mathematics graph calculation formula: 1 Square C perimeter S area a side length perimeter = side length * 4 C = 4a area = side length * side length S = a * a 2 Cube V: Volume a: Edge length Surface area = Edge length * Edge length * 6 S table = a * a * 6 Volume = Edge length * Edge length * Edge length V = a * a * a 3 Rectangle C Perimeter S Area a Side length and perimeter = (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 = (length*width+length*height+width*height)*2 S=2(ab+ah+bh) (2) Volume=length*width*height V=abh 5 Triangle s area a base h height area=base* Height ÷ 2 s = ah ÷ 2 Triangle height = area * 2 ÷ base Triangle base = area * 2 ÷ height 6 Parallelogram s area a base h height area = base * height s = ah 7 Trapezoid s area a upper base b lower Base h height area = (upper base + lower base) * height ÷ 2 s = ( a + b ) * h ÷ 2 8 Circle S area C perimeter π d = diameter r = radius (1) perimeter = diameter * π=2*π*radius C=πd=2πr (2) Area=radius*radius*n 9 Cylinder v: volume h: height s; base area r: base radius c: base perimeter (1) side area = Base perimeter * height (2) Surface area = side area + base area * 2 (3) Volume = base area * height (4) Volume = side area ÷ 2 * radius 10 Cone v: volume h: height s; base area r: Base radius volume = base area * height ÷ 3 The formula for the sum and difference problem: Total number ÷ total number of copies = average (sum + difference) ÷ 2 = large number (sum - difference) ÷ 2 = sum of decimals and times problem ÷ (Multiple times - 1) = decimal decimal * multiple = large number (or sum - decimal = large number) Difference problem ÷ (multiple - 1) = decimal decimal * multiple = large number (or decimal + difference = large number) Planting trees Question 1 The problem of tree planting on non-closed lines can be mainly divided into the following three situations: ⑴ If trees are to be planted at both ends of the non-closed lines, then: Number of plants = Number of sections + 1 = Full length ÷ Plant spacing - 1 Full length = Plant spacing * (Number of plants - 1) Plant spacing = Full length ÷ (Number of plants - 1) ⑵ If you want to plant trees at one end of the non-closed line and not plant trees at the other end, then: Number of plants = Number of sections = Full length ÷ Plant spacing Full length = Plant spacing * Number of plants Plant spacing = Full length Length ÷ Number of plants ⑶ If no trees are planted at both ends of the non-closed line, then: Number of plants = Number of segments - 1 = Full length ÷ Plant spacing - 1 Full length = Plant spacing * (Plant number + 1) Plant spacing = Full length ÷ (Plant number + 1) 2 The quantitative relationship of tree planting problems on closed lines is as follows: number of plants = number of sections = full length ÷ spacing between plants. Total length = spacing between plants * number of plants. Spacing between plants = total length ÷ number of plants. Profit and loss problem (profit + loss) ÷ difference between the two allocations = participation in the allocation. Number (big profit - small profit) ÷ difference between the two distribution amounts = number of shares participating in the distribution (big loss - small loss) ÷ difference between the two distribution amounts = number of shares participating in the distribution Encounter problem encounter distance = speed sum * encounter Time meeting time = meeting distance ÷ speed and sum of speed = meeting distance ÷ meeting time catch-up problem catch-up distance = speed difference * catch-up time catch-up time = catch-up distance ÷ speed difference speed difference = catch-up distance ÷ catch-up time flow problem downstream speed = still water Speed ??+ water flow speed counter current speed = static water speed - water flow speed static water speed = (downstream speed + counter current speed) ÷ 2 water flow speed = (downstream speed - counter current speed) ÷ 2 concentration problem weight of solute + weight of solvent = solution Weight Weight of solute ÷ weight of solution * 100% = concentration Weight of solution * concentration = weight of solute Weight of solute ÷ concentration = weight of solution Profit and discount problem Profit = selling price - cost Profit margin = profit ÷ cost * 100 %= (sold price ÷ cost - 1) * 100% increase or decrease amount = principal * increase or decrease percentage discount = actual selling price ÷ original selling price * 100% (discount interest = principal * interest rate * time after-tax interest = Principal * Interest rate * Time * (1-20%) Sum of edge lengths: Sum of edge lengths of a cuboid = (Length + Width + Height) Sum of edge lengths of a cube = Edge length * 12 Memorize the following positive and inverse proportional relationships: Direct proportional relationship: Square The circumference of a rectangle is directly proportional to the length of its side. The circumference of a rectangle is directly proportional to its length. The circumference of a circle is directly proportional to its diameter. The circumference of a circle is directly proportional to its radius. The area of ??a circle is directly proportional to the square of its radius. Commonly used Quantity relationship: 1. Distance = speed * time Speed ??= distance ÷ time Time = distance ÷ speed Total amount of work = work efficiency * working time Work efficiency = total amount of work ÷ working time Working time = total amount of work ÷ total work efficiency = Unit price * quantity Unit price = total price ÷ quantity quantity = total price ÷ unit price total output = unit output * area unit output = total output ÷ area area = total output ÷ unit output Unit conversion: length unit: one kilometer = 1 kilometer = 1000 Meter 1 meter = 10 decimeters 1 decimeter = 10 centimeters 1 centimeter = 10 millimeters Area unit: 1 square kilometer = 100 hectares 1 hectare = 100 acres 1 acre = 100 square meters 1 square kilometer = 1,000,000 square meters 1 hectare = 10,000 square meters 1 square meter = 100 square decimeters 1 square decimeter = 100 square centimeters 1 square centimeter = 100 square millimeters Volume unit: 1 cubic kilometer = 1000000000 cubic meters 1 cubic meter = 1000 cubic decimeters 1 cubic minute Meter = 1000 cubic centimeters 1 cubic centimeter = 1000 cubic millimeters 1 cubic decimeter = 1 liter 1 cubic centimeter = 1 ml 1 liter = 1000 ml Weight unit: 1 ton = 1000 kilograms 1 kilogram = 1000 grams Time unit: one century = 100 One year = four quarters One year = 12 months One year = 365 days (normal year) One year = 366 days (leap year) One quarter = 3 months One month = 3 ten days (upper, middle, lower) One month = 30 days (Small month) One month = 31 days (Big month) One week = 7 days One day = 24 hours One hour = 60 minutes One minute = 60 seconds Big months in the year: January, March, May, July , August, October, December (seven months) Small months of the year: April, June, September, November (four months) Special fraction value: =0.5=50% = 0.25 = 25% = 0.75 = 75% = 0.2 = 20% = 0.4 = 40% = 0.6 = 60% = .