1, number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.

2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple

3. Speed × time = distance/speed = time/distance/time = speed.

4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price

5 working efficiency × working time = total work amount ÷ working efficiency = working time ÷ total work amount ÷ working time = working efficiency

6. Appendix+Appendix = sum, and-one addend = another addend.

7. Minus-Minus = Minus-Minus = Minus+Minus = Minus

8. Factor × factor = product ÷ one factor = another factor.

9. Dividend = quotient dividend = divisor quotient × divisor = dividend

Calculation formula of mathematical graphics in primary schools

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: side 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 (c: perimeter s: area a: 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 (length× width+length× height+width× height )× 2s = 2 (AB+ah+BH)

(2) volume = length× width× height V=abh

5. Triangle (S: area A: base H: height)

Area = bottom × height ÷2 s=ah÷2

Height of triangle = area ×2÷ base of triangle = area ×2÷ height

6. parallelogram (s: area a: bottom h: height)

Area = bottom × height s=ah

7. trapezoid (s: area a: upper bottom b: lower bottom h: height)

Area = (upper bottom+lower bottom) × height ÷2 s=(a+b)× h÷2.

8. Circle (s: area c: perimeter л d= diameter r= radius)

(1) perimeter = diameter× л = 2×л× radius C=лd=2лr

(2) area = radius × radius× л

9. Cylinder (V: volume H: height S: bottom area R: bottom radius C: bottom circumference)

(1) lateral area = bottom perimeter × height =ch(2лr or лd) (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

1 1, total number of copies/total number of copies = average.

12, the formula of sum and difference problem

(sum+difference) ÷ 2 = large number (sum-difference) ÷ 2 = decimal.

13 and the question of time

Sum ÷ (multiple-1) = decimal × multiple = large number (or sum-decimal = large number)

14, differential time problem

Difference ÷ (multiple-1) = decimal × multiple = large number (or decimal+difference = large number)

15, encountered a problem.

Meeting distance = speed × meeting time

Meeting time = meeting distance/speed and

Speed sum = meeting distance ÷ meeting time

16, 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.

17, profit and discount

Profit = selling price-cost

Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.

Up and down amount = principal × up and down percentage

Interest = principal × interest rate× time

After-tax interest = principal × interest rate × time × (1-20%)

Universal unit conversion

Length unit conversion

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

Area unit conversion

1 square kilometer = 100 hectare 1 hectare = 10000 square meter 1 square meter = 100 square decimeter.

1 dm2 = 100 cm2 1 cm2 = 100 mm2

Volume (volume) unit conversion

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

1 cm3 = 1 ml 1 m3 = 1000 liter

Weight unit conversion

1t = 1000kg 1kg = 1000g 1kg = 1kg。

Rmb unit conversion

1 yuan = 10 angle 1 angle = 10 point 1 yuan = 100 point.

Time unit conversion

1 century = 100 1 year =1February (3 1 day) has:1\ 3 \ 5 \ 7 \ 8 \1.

February 28th in a normal year and February 29th in a leap year: 365 days in a normal year and 366 days in a leap year: 1 =24 hours.

1 hour = 60min 1 minute = 60s 1 hour = 3600s.

basic concept

Chapter I Number and Number Operation

A concept

(1) integer

3 counting unit

One, ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units.

The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.

Divisibility of 5 numbers

When the integer A is divided by the integer b(b ≠ 0), the quotient is an integer with no remainder, so we say that A is divisible by B, or that B is divisible by A. ..

If the number A is divisible by the number B (b ≠ 0), then A is called a multiple of B, and B is called a divisor of A (or a factor of A). Multiplication and divisor are interdependent.

Because 35 is divisible by 7, 35 is a multiple of 7, and 7 is a divisor of 35.

The divisor of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself. For example, the divisor of 10 is 1, 2,5, 10, where the smallest divisor is 1 0 and the largest divisor is 10.

The number of multiples of a number is infinite, and the smallest multiple is itself. The multiple of 3 is: 3, 6, 9, 12 ... The minimum multiple is 3, but there is no maximum multiple.

Numbers in units of 0, 2, 4, 6 and 8 can be divisible by 2, for example, 202, 480 and 304 can be divisible by 2. .

A number of 0 or 5 can be divisible by 5, and the sum of a number can be divisible by 3. The sum of each digit of a number can be divisible by 9, and so can this number.

A number divisible by 2 is called an even number.

Numbers that are not divisible by 2 are called odd numbers.

0 is also an even number. Natural numbers can be divided into odd and even numbers according to their divisibility by 2.

A number with only two divisors of 1 is called a prime number (or prime number), and the prime numbers within 100 are: 2, 3, 5, 7,1,13, 17.

If a number has other divisors besides 1 and itself, then it is called a composite number. For example, 4, 6, 8, 9 and 12 are all complex numbers.

1 is not a prime number or a composite number, and natural numbers are either prime numbers or composite numbers except 1. If natural numbers are classified according to the number of their divisors, they can be divided into prime numbers, composite numbers and 1.

Every 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. For example, 15=3×5, and 3 and 5 are called prime factors of 15.

Multiplying a composite number by a prime factor is called prime factor decomposition.

For example, decompose 28 into prime factors.

The common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor of these numbers. For example, the divisor of 12 is 1, 2, 3, 4, 6,12; The divisors of 18 are 1, 2,3,6,9 and 18. Where 1, 2,3,6 are the common divisors of 12 and 1 8, and 6 is their greatest common divisor.

The common divisor is only 1, which is called prime number. There are the following situations:

1 is coprime with any natural number.

Two adjacent natural numbers are coprime.

Two different prime numbers are coprime.

When the composite number is not a multiple of the prime number, the composite number and the prime number are coprime.

When the common divisor of two composite numbers is only 1, these two composite numbers are coprime. If any two numbers are coprime, they are said to be coprime.

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. For example, the multiple of 2 is 2,4,6,8, 10, 12, 14, 16, 18. ...

The multiple of 3 is 3,6,9, 12, 15, 18 ... where 6, 12, 18 ... are the common multiples of 2 and 3, and 6 is their least common multiple. .

If the larger number is a multiple of the smaller number, the larger number is the least common multiple of the two numbers.

If two numbers are prime numbers, then the product of these two numbers is their least common multiple.

The common divisor of several numbers is finite, while the common multiple of several numbers is infinite.

(3) scores

1 significance of the score

Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction.

2 Reduction and comprehensive score

Changing a fraction into a fraction equal to it, but with smaller numerator and denominator, is called divisor.

The denominator of a molecule is a fraction of a prime number, which is called simplest fraction.

Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.

Three properties and laws

(4) the basic nature of the score: the numerator and denominator of the score are multiplied or divided by the same number (except zero), and the size of the score remains unchanged.

(7) Common quantitative relations:

Total price = unit price × quantity

Distance = speed × time

Total amount of work = working time × working efficiency

Total output = single output × quantity

Tree planting problem:

Law of problem solving: plant trees along the line.

Tree = number of segments+1 tree = total distance ÷ distance between plants+1

Plant spacing = total distance ÷ (tree-1) total distance = plant spacing × (tree-1)

Planting trees along the periphery

Tree = total distance ÷ plant distance

Plant spacing = total distance.

Total distance = plant spacing × trees

(13) chicken and rabbit problem: the law of solving problems: (total number of legs-number of chicken legs × total number of heads) ÷ the difference between the number of legs of a chicken and rabbit = the number of rabbits.

Number of rabbits = (total number of legs -2× total number of heads) ÷2

If we assume all rabbits, we can have the following formula:

Number of chickens =(4× total number of heads-total number of legs) ÷2

Number of rabbits = total-number of chickens

Chicken and rabbit pass 50 heads 170 legs. How many chickens and rabbits are there?

The number of rabbits is (170-2 × 50 )÷ 2 =35 (only).

The number of chickens is 50-35= 15 (only)

4 Attendance rate

Germination rate = number of germinated seeds/number of experimental seeds × 100%

Wheat flour yield = flour weight/wheat weight × 100%.

Product qualification rate = number of qualified products/total number of products × 100%.

Employee attendance = actual attendance/attendance × 100%

Five engineering problems:

Quantitative relationship:

Total amount of work = working efficiency × working time

Work efficiency = total workload ÷ working hours

Working hours = total amount of work ÷ working efficiency

Total workload ÷ work efficiency = cooperation time

Interest = principal × interest rate× time

Chapter II Weights and Measures

(3) conversion of area units

* 1 cm2 =100mm2 * 1 cm2 =1cm2 * 1 m2 =100mm2.

* 1 ha = 10000 m2 * 1 km2 = 100 ha.

(3) 2 unit of volume conversion

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

* 1 l = 1 m3 * 1 ml = 1 cm3.

(3) General conversion

* one ton = 1000 kg

* 1 kg =1000g

quintic

(1) What is time?

Refers to a period of time with a starting point and an ending point.

(2) Common units

Century, year, month, day, hour, minute and second.

(3) Unit conversion

* 1 century = 100 year

* 1 year = average number of years of 365 days.

* One year =366 days leap year

* January, Wednesday, Friday, July, August, October and December are big months, with 3 1 day.

* Four, six, nine and eleven are abortions. Abortion lasts for 30 days.

* There are 28 days in February in a normal year and 29 days in February in a leap year.

* 1 day = 24 hours

* 1 hour =60 points

* One minute =60 seconds

Six currencies

(1) What is money?

Money is a special commodity, which acts as the equivalent of all commodities. Money is a general representative of value and can buy any other commodity.

(2) Common units

* Yuan * Jiao * fen

(3) Unit conversion

* 1 yuan = 10 angle.

* 1 angle = 10 point

(1) Common quantitative relations

The distance is represented by s and the speed by t, and the relationship between them is as follows:

t=s/v

The total price is represented by A, the unit price is represented by B, and the quantity is represented by C. The relationship between them is as follows:

A = BC

B = air conditioning

c=a/b

The radius of a circle is represented by R, the diameter by D, the circumference by C and the area by S.

c=∏d=2∏r

s=∏ r？

The radius of the sector is represented by r, n is the degree of the central angle, and the area is represented by s.

s=∏ nr？ /360

The height of the cylinder is represented by H, the circumference of the bottom is represented by C, the area of the bottom is represented by S, and the volume is represented by V. 。

S side =ch

S table =s side +2s bottom

v=sh