Basic formula:
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
seven
-Subtraction = Difference
-Difference = negative
Difference+subtraction =
8 factor × factor = product
Product ÷ One factor = another factor
nine
Divider = quotient
Quotient = divisor
Quotient × divisor =
Graphic calculation formula:
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 = (length× width+length× height+width× height) ×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
= area × 2 dida
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 π d= diameter r= radius
(1) circumference = diameter ×π=2×π× radius
C=πd=2πr
(2) area = radius × radius ×n
nine
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
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area × height ÷3
The formula is:
Total number ÷ Total number of copies =
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or sum-decimal = large number)
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or decimal+difference = large number)
1 open circuit
Mainly 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)
2. Close the circuit
about
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
(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.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
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
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 and discount problem
Profit = selling price-cost
= 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%)
Sum of side lengths:
Length of cuboid = (length+width+height)
Cube side length = side length × 12
Remember the following affirmation.
The perimeter and side length of a square.
The circumference of a rectangle is equal to (length+width)
The circumference of a circle is equal to its diameter.
relationship
The circumference of a circle is equal to the radius.
relationship
The area of a circle is the square of the radius.
relationship
frequently-used
1. Distance = speed × time speed = distance/time/time = distance/speed.
Total workload = working efficiency × working time = total workload ÷ working time = total workload ÷ working efficiency.
Total price = unit price × quantity unit price = total price/quantity = total price/unit price.
Total output = single output × single output per unit area = total output/area = total output/single output
One kilometer = 1 km = 1 000m 1 m = 1 decimeter1decimeter =10cm10mm.
1
= 100 ha 1 ha = 100 ha
1
= 100 m2
1
= 1000000 square meters 1 hectare = 10000 square meters 1 square meter = 100 square decimeter.
1 dm2 = 100 cm2 1 cm2 = 100 mm2
1
= 100000000 m3 1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter.
1 cm3 = 1000
1 cubic decimeter = 1 liter 1 cubic centimeter = 1 ml 1 liter = 1000 ml.
Bit:
1 ton = 1 000kg1kg =1000g
Century = 100 = fourth quarter year =65438+ February year =365 days (
) One year =366 days (
)
The first quarter =3 months a month =30 days (up, middle and down) a month = 30 days (
) One month =3 1 day (big month)
A week = 7 days a day = one hour and 24 hours =60 minutes =60 seconds.
Big months of the year: January, March, May, July, August, October and December (seven months).
A year later.
April, June, September and November (four months)
special
=0.5=50% = 0.25 = 25% = 0.75 = 75%
= 0.2 = 20% = 0.4 = 40% = 0.6 = 60% = 0.8 = 80%
=0. 125= 12.5% = 0.375 = 37.5% = 0.625 = 62.5% = 0.875 = 87.5%
arithmetic
1、
: two numbers are added to exchange the position of the addend, and the sum is unchanged. (2) What do you respect most about the humble, and why?
2、
:a + b = b + a
3、
:a × b = b × a
4、
:a × b × c = a ×(b × c)
5、
:a × b + a × c = a × b + c
6. The nature of division: a ÷ b ÷ c = a ÷(b × c)
7. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide o by any number that is not o to get o. Simple multiplication:
、
Multiply with the o at the end. You can multiply 1 before o first. Zero does not participate in the operation, and several zeros are added at the end of the product.
8. Division with remainder: dividend = quotient × divisor+remainder
Equations, Algebras and Equality
Equation: An equation in which the value on the left of the equal sign equals the value on the right of the equal sign is called an equation. Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.
Equation: An equation with an unknown number is called an equation.
Equation: An equation that contains an unknown number and the degree of this unknown number is 1
Type. study
Example method and formula calculation. That is, an example is given to illustrate that the formula is replaced by χ and calculated.
Algebra: Algebra means replacing numbers with letters.
: use
The formula shown is called
. For example 3x = AB+C.
mark
Fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.
Comparison of fraction size: Compared with the fraction of denominator, the numerator is large and the numerator is small. First, compare the scores of different denominators.
Then compare; If the numerator is the same, the denominator is big and small.
Fraction. Fraction.
Then: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. First, add and subtract fractions with different denominators.
Then add and subtract.
Fraction multiplied by integer, numerator is the product of fractional and integer multiplication, denominator remains unchanged.
Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
Law of fractional addition and subtraction: Fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator remains the same. First, add and subtract fractions with different denominators.
Then add and subtract.
The concept of reciprocal: 1 If the product of two numbers is 1, we call one of them the reciprocal of the other. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.
A fraction divided by an integer (except 0) is equal to this fraction multiplied by the reciprocal of this integer.
: 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.
The law of division of fractions: dividing by a number (except 0) is equal to multiplying the reciprocal of this number.
The fraction of numerator less than denominator is called
.
A fraction whose numerator is greater than the denominator or whose numerator and denominator are equal is called.
Greater than or equal to 1.
Write a false fraction as the sum of integers
The form of, called
.
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.
A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
The number A divided by the number B (except 0) is equal to the reciprocal of the number A multiplied by the number B.
computing formula
Unit price × quantity = total price 2, single output × quantity = total output
Speed × time = distance 4, work efficiency × time = total workload.
Appendix+Appendix = and one addend = and+another addend.
Negative-negative = differential negative = negative-differential negative = negative+difference.
Factor × factor = product One factor = product ÷ another factor.
Frequency divider/frequency divider = frequency divider = frequency divider/frequency divider = quotient × frequency divider
compare
What is the ratio? When two numbers are divided, it is called the ratio of two numbers. For example, the ratio of 2÷5 or 3:6 or 1/3 is multiplied or divided by the same number at the same time, and the ratio remains unchanged.
What is proportion? Two formulas with equal ratios are called proportions. For example, 3: 6 = 9: 18
The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.
The unknown item in the proportion is called
. Such as 3: χ = 9: 18.
Proportion: two related quantities, one of which changes and the other changes. If the ratio (i.e. quotient k) corresponding to these two quantities is constant, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k( k must be) or kx = y.
Two related quantities, one of which changes and the other changes with it. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called processes.
The relationship between them is called
. For example: x×y = k( k must be) or k/x = y.
A number indicating that one number is a percentage of another number is called.
. Percentages are also called percentages or percentages.
To convert the decimal point into a percentage, just move the decimal point two places to the right and add it to the back.
. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%. Turn the percentage into a decimal, and put
Delete it and move the decimal point two places to the left.
To convert a fraction into a percentage, the fraction is usually converted into a decimal (usually reserved when it is not used up)
), and then turn the decimal into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%.
Convert the percentage into the number of components, and rewrite the percentage into the number of components first.
offer a price
.
Learn how to convert fractions into fractions and how to convert fractions into decimals.
Multiples and divisors
The common divisor of several numbers is called the divisor of these numbers.
The quantity is limited. The biggest one is called these numbers.
.
Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are infinite common multiples. The smallest one is called the least common multiple of these numbers.
：
1 has only two numbers, which are called
. Two adjacent numbers must be prime numbers. Two consecutive odd numbers must be coprime. 1 and any number coprime.
Comprehensive score: the difference between scores of different denominators is changed into the same denominator score equal to the original score, which is called comprehensive score. (Common divisor is the least common multiple)
Divide the numerator and denominator of a fraction by.
Constant, this process is called
.
The numerator and denominator are
The score is called
. At the end of the score calculation, the number of people must be reduced to the maximum.
.
Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
separable
If c | a, c | b, then c | (a b)
If, then b | a, c | a
If b | a, c | a and (b, c)= 1, then BC | a.
If c | b, b | a, then c | a
A number is called if it has other divisors besides 1 and itself.
. 1 is not a prime number, nor is it.
.
If a prime number is a factor of a certain number, then this prime number is this number.
.
: use complex numbers
The way to express each other is called
.
Multiple characteristics:
Characteristics of multiples of 2: You are 0, 2, 4, 6, 8.
Characteristics of multiples of 3 (or 9): The sum of the numbers on each digit is multiples of 3 (or 9).
Characteristics of multiples of 5: You are 0, 5.
Characteristics of multiples of 4 (or 25): The last two digits are multiples of 4 (or 25).
Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125).
Characteristics of multiples of 7 (1 1 or 13): the difference (big-small) between the last three digits and other digits is a multiple of 7 (1 1 3).
Characteristics of multiples of 17 (or 59): the difference (big-small) between the last three digits and the rest digits is a multiple of 17 (or 59).
Characteristics of multiples of 19 (or 53): the difference (big-small) between the last three digits and other seven digits is a multiple of 19 (or 53).
Characteristics of multiples of 23 (or 29): The difference (big-small) between the last four digits and the other five digits is multiples of 23 (or 29).
Two numbers of multiple relations,
It's a small number, and the least common multiple is a big number.
The coprime relation between two numbers, the greatest common divisor is 1, and the least common multiple is the product.
When two numbers are divided by their greatest common divisor, the quotient is coprime.
The product of two numbers and the least common multiple is equal to the product of these two numbers.
The common divisor of two numbers must be the greatest common divisor of these two numbers.
1 is neither prime nor composite.
A prime number greater than 3 divided by 6 must get 1 or 5.
Odd and even numbers
Even numbers: Numbers are numbers of 0, 2, 4, 6 and 8.
Odd number: The number is not 0, 2, 4, 6 or 8.
Even even = even Qiqi = Qiqi.
Even numbers add up to even numbers, and odd numbers add up to odd numbers.
Even × even = even × odd = odd × even = even.
The sum of two adjacent natural numbers is odd, and the product of adjacent natural numbers is even.
If one number in the multiplication is even, then the product must be even.
Odd ≠ even number
decimal
Natural number: an integer used to represent the number of objects, called natural number. 0 is also a natural number.
: The unit is a decimal of 0.
With Decimal: Decimal with more than 0 digits.
: a decimal, starting from somewhere in the decimal part, and a number or numbers are repeated in turn. Such a decimal is called
. Like 3. 14 14 14.
no
A decimal, starting from the decimal part, without one number or several numbers appearing repeatedly, is called acyclic decimal. Like 3. 14 1592654.
Infinite cycle decimal: a decimal, from the decimal part to the infinite digits, and one or several numbers are repeated in turn. Such decimals are called infinite cyclic decimals. For example, 3. 14 14 14 ...
A decimal, from the decimal part to the infinite digits, without one number or several numbers repeating in turn, is called
. Such as 3. 14 1592654. ...
profit
Interest = principal × interest rate × time (time is usually in years or months, which should correspond to the unit of interest rate).
Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal for a year is called
. The ratio of interest to principal in January is called
.
Internal angle sum
When the number of sides is -2 times 180 or more, it is copy and paste. The whole book. Hope to adopt