Party A and Party B work together in 12 days. If Party A works alone in 8 days, the rest of Party B can work alone in 18 days

Party A and Party B work together in 12 days. If Party A works alone in 8 days, the rest of Party B can work alone in 18 days

8 / x + 18 (1 / 12-1 / x) = 18 / x + 1.5-18 / x = 110 / x = 1 / 2
If Party A completes in X days, Party B completes in 1 / 12-1 / X days. According to the topic,
8/X +18(1/12-1/X)=1
8/X +1.5-18/X=1
10/X=1/2
X=20
Because a completed alone 20 days, so a's work efficiency is 1 / 20, work efficiency: the total amount of work divided by the working hours, usually the total work... To start
If Party A completes in X days, Party B completes in 1 / 12-1 / X days. According to the topic,
8/X +18(1/12-1/X)=1
8/X +1.5-18/X=1
10/X=1/2
X=20
Because party a completes the work in 20 days alone, Party A's work efficiency is 1 / 20. Work efficiency: the total amount of work divided by the working time. Generally, the total amount of work is in the unit of "1", so, the efficiency of Party B is 1 / 12-1 / 20 = 1 / 30
A: the efficiency of a is 1 / 20, and that of B is 1 / 30. Put it away
A alone X days to complete
B 1 / 12-1 / X
8/X +18(1/12-1/X)=1
8/X +1.5-18/X=1
10/X=1/2
X=20
1/12-1/20=1/30
The efficiency of a is 1 / 20
The efficiency of B is 1 / 30
Convert mathematical expression to C + + expression (very simple)
（a+b)/(a-b) (a+b)/(c+d) a
1:
(a+b)/(a-b);
2:
(a+b)/(c+d);
3:
A
If the direction of your figure in the sun is 35 degrees north by west, then the direction of the sun is relative to you
35 degrees south by East
How to count the total by frequency
Total = frequency * frequency
The relationship among frequency, frequency and total number
There are three formulas to write
Frequency = frequency △ total
Frequency = total number × frequency
Total number = frequency △ frequency
How to calculate frequency and frequency
Frequency is the number of times an event occurs: for example, 10 out of 20 balls are randomly selected, and there are 6 yellow balls. 6 is the frequency of yellow balls. 6 / 20 is the frequency of yellow balls, that is, frequency / total
Generally speaking, the number of data in different groups is the frequency of the group, and the ratio of the frequency to the total number is the frequency.
Select a frequency and its corresponding frequency. Divide the frequency by the frequency to get the total number. Divide the total number by several frequencies to get the average number. For example, 5, 4, 3 and 8 are frequencies, then the frequency is 0.25, 0.2,
The relationship between frequency, frequency and total number of experiments is ()
A. The greater the frequency is, the greater the frequency is. B. when the total number of times is fixed, the greater the frequency is, and the frequency can be infinite. C. The frequency is directly proportional to the total number of times. D. when the frequency is fixed, the frequency is inversely proportional to the total number of times
A. If the frequency is larger and the total number is larger, the frequency is not necessarily large, so the option is wrong; B. if the frequency is less than or equal to 1, then the option is wrong; C. if the frequency is fixed, the frequency is proportional to the total number, so the option is wrong; D. if it is correct, then select D
All mathematical formulas for Primary School Grades 1-6
Junior high school learning needs. Kneel to beg!
Volume and surface area
The area of triangle = base × height △ 2. Formula s = a × h △ 2
Square area = side length × side length formula s = A2
The area of rectangle = length × width formula s = a × B
The area of parallelogram = base × height formula s = a × H
Area of trapezoid = (upper bottom + lower bottom) × height △ 2 Formula s = (a + b) H △ 2
Sum of internal angles: sum of internal angles of triangle = 180 degrees
Surface area of cuboid = (length × width + length × height + width × height) × 2 Formula: S = (a × B + a × C + B × C) × 2
Surface area of cube = edge length × edge length × 6 formula: S = 6A2
Cuboid volume = length × width × height formula: v = ABH
Cuboid (or cube) volume = base area × height formula: v = ABH
Volume of cube = edge length × edge length × edge length formula: v = A3
The formula of circle circumference = diameter × π: l = π d = 2 π R
The area of circle = radius × radius × π formula: S = π R2
Surface (side) area of a cylinder: the surface (side) area of a cylinder is equal to the circumference of the bottom multiplied by the height. Formula: S = ch = π DH = 2 π RH
Surface area of a cylinder: the surface area of a cylinder is equal to the circumference of the bottom multiplied by the height plus the area of the circles at both ends. Formula: S = ch + 2S = ch + 2 π R2
Volume of cylinder: the volume of cylinder is equal to the area of bottom multiplied by height. Formula: v = sh
The volume of the cone is 1 / 3 of the bottom surface × the product height. The formula is v = 1 / 3SH
arithmetic
1. Additive commutative law: two numbers are added to exchange the position of addends, and the sum remains unchanged
2. Additive combination law: a + B = B + A
3. Commutative law of multiplication: a × B = B × a
4. Multiplicative Association Law: a × B × C = a × (B × C)
5. Multiplicative distribution law: a × B + a × C = a × B + C
6. The nature of division: a △ B △ C = a △ (B × C)
7. The nature of division: in division, the divisor and the divisor expand (or reduce) the same multiple at the same time, and the quotient remains unchanged. O divided by any number that is not o will get O. simple multiplication: for multiplication with o at the end of the multiplicator and multiplicator, the multiplication before o can be carried out first, and the zero will not participate in the operation, and several zeros will fall and be added at the end of the product
8. Division with remainder: dividend = quotient × divisor + remainder
Equation, algebra and equality
Equation: an equation in which the value on the left side of the equal sign is equal to the value on the right side of the equal sign is called an equation. Basic properties of the equation: if both sides of the equation multiply (or divide) the same number at the same time, the equation still holds
Equations: Equations with unknowns are called equations
Unary linear equation: an equation containing an unknown number and the number of unknowns is once is called unary linear equation. Learn the example method and calculation of unary linear equation. That is to say, give an example and calculate the formula with χ
Algebra: algebra is the substitution of letters for numbers
Algebraic formula: a formula expressed in letters is called an algebraic formula. For example, 3x = AB + C
fraction
Fraction: the unit "1" is divided into several parts equally, representing such a fraction or fraction
Comparison of fractions: compared with fractions with the same denominator, fractions with larger numerator are larger and fractions with smaller numerator are smaller. Compared with fractions with different denominators, fractions with the same denominator are divided first and then compared. If the numerator is the same, fractions with larger denominator are smaller
The law of addition and subtraction of fractions: add and subtract fractions with the same denominator, only add and subtract molecules with the same denominator. Add and subtract fractions with different denominators, and then add and subtract
The numerator is the product of the numerator of a fraction multiplied by an integer, with the denominator unchanged
A fraction multiplied by a fraction uses the product of multiplication of molecules as the numerator and the product of multiplication of denominators as the denominator
The law of addition and subtraction of fractions: the fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator is not changed. The fractions with different denominators are added and subtracted first, and then added and subtracted
The concept of reciprocal: 1. If the product of two numbers is 1, we call one the reciprocal of the other. These two numbers are reciprocal to each other. The reciprocal of 1 is 1, 0 has no reciprocal
A fraction divided by an integer (except 0) is a fraction multiplied by the reciprocal of the integer
The basic properties of fraction: the numerator and denominator of fraction multiply or divide by the same number (except 0), the size of fraction
Division of fractions: dividing by a number (except 0) is equal to multiplying the reciprocal of the number
True fraction: fraction whose numerator is smaller than denominator is called true fraction
False fraction: fraction whose numerator is larger than denominator or whose numerator and denominator are equal is called false fraction. False fraction is greater than or equal to 1
With fraction: the false fraction written in the form of integer and true fraction is called with fraction
Basic properties of fraction: the numerator and denominator of fraction multiply or divide by the same number (except 0), and the size of fraction remains unchanged
Calculation formula of quantity relation
Unit price × quantity = total price 2. Unit output × quantity = total output
Speed × time = distance 4, work efficiency × time = total amount of work
Addend + addend = and one addend = and + another addend
Subtracted - subtracted = subtracted = subtracted - subtracted = subtracted + subtracted
Factor × factor = product one factor = product △ another factor
Divisor / divisor = quotient divisor = divisor / quotient divisor = quotient × divisor
Length unit:
1km = 1km 1km = 1000M
1 meter = 10 decimeter 1 decimeter = 10 cm 1 cm = 10 mm
area unit:
1 square kilometer = 100 hectares 1 hectare = 10000 square meters
1 square meter = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter
1 mu = 666.666 square meters
Volume unit
1 cubic meter = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter
1 cubic centimeter = 1000 cubic millimeter
1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter
weight
1t = 1000kg 1kg = 1000g = 1kg = 1kg
than
What is ratio: the division of two numbers is called the ratio of two numbers. For example, if the preceding and the following terms of the ratio of 2 / 5 or 3:6 or 1 / 3 are multiplied or divided by the same number (except 0), the ratio will not change
What is the ratio: the formula that indicates that two ratios are equal is called the ratio. For example, 3:6 = 9:18
The basic nature of proportion: in proportion, the product of two external terms equals the product of two internal terms
Solution proportion: finding the unknown term in the proportion is called solution proportion. For example, 3: χ = 9:18
Positive proportion: two related quantities, one of which changes and the other changes. If the corresponding ratio (i.e. quotient K) of the two quantities is fixed, the two quantities are called positive proportion quantities, and their relationship is called positive proportion relations. For example, Y / x = K (k is fixed) or KX = y
Inverse proportion: two related quantities, one of which changes, and the other changes with it. If the product of the two numbers corresponding to the two quantities is fixed, the two quantities are called inverse proportion quantities, and their relationship is called inverse proportion relations. For example, X × y = K (k is fixed) or K / x = y
percentage
Percentage: a number that represents the percentage of one number to another is called percentage. Percentage is also called percentage or percentage
To convert a decimal into a percentage, just move the decimal point two places to the right and add a percentage sign after it. In fact, to convert a decimal into a percentage, just multiply the decimal by 100%. To convert a percentage into a decimal, just remove the percentage sign and move the decimal point two places to the left
To convert fractions into percentages, we usually convert fractions into decimals first (three decimal places are usually reserved when there is not enough Division), and then convert decimals into percentages. In fact, to convert fractions into percentages, we should first convert fractions into decimals, and then multiply them by 100%
Change percentage into fraction, first rewrite percentage into fraction, and those that can be reduced into simplest fraction
We should learn how to change decimal into fraction and how to change fraction into decimal
Multiple and divisor
Greatest common divisor: the common divisor of several numbers is called the common divisor of these numbers. There are finite common factors. The largest one is called the greatest common divisor of 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
Coprime number: two numbers with only one common divisor are called coprime numbers. Two adjacent numbers must be coprime. Two consecutive odd numbers must be coprime. 1 and any number must be coprime
General division: the division of fractions with different denominators into fractions with the same denominator, which are equal to the original fraction, is called general division
Reduction: divide the numerator and denominator of a fraction by the common divisor at the same time, and the value of the fraction remains unchanged. This process is called reduction
Minimalist fraction: the fraction whose numerator and denominator are coprime numbers is called minimalist fraction. At the end of fraction calculation, the result must be reduced to minimalist fraction
Prime: a number is called prime if it has only one and two divisors
Composite number: a number is called composite if it has other divisors besides 1 and itself. 1 is neither prime nor composite
quality