Elementary school mathematics formula (1)
First, the problem of sum and difference
Given the sum and difference of two numbers, find these two numbers.
Formula:
And the sum and the difference are getting bigger and bigger;
Divided by 2, it is big;
And subtract the difference, the smaller the reduction;
Divided by 2, it is small.
Example: It is known that the sum of two numbers is 10, and the difference is 2. Find these two numbers.
According to the formula, large number =( 10+2)/2=6, and decimal number =( 10-2)/2=4.
Second, the problem of chickens and rabbits in the same cage.
Formula:
Suppose all chickens, suppose all rabbits.
How many feet are there? How many feet are missing?
Divided by the foot difference, it is the number of chickens and rabbits.
Example: chickens are free in the same cage, with head 36 and feet 120. Find the number of chickens and rabbits.
When finding rabbits, it is assumed that they are all chickens, so the number of exempted children =( 120-36X2)/(4-2)=24.
When looking for chickens, it is assumed that they are all rabbits, so the number of chickens = (4x36-120)/(4-2) =12.
Mathematical formula for primary schools (2)
Third, the concentration problem.
(1) diluted with water
Formula:
Sugar before adding water, sugar water after adding sugar.
Sugar water MINUS sugar water is the amount of sugar added.
Example: There is 20kg of sugar water with the concentration of 15%. How many kilograms of water are added, and the concentration becomes 10%.
Get the sugar before adding water. The original sugar content is 20X 15%=3 (kg).
When the sugar is used up, how much sugar water should there be with the concentration of 10%? 3/ 10%=30 (kg).
Sugar water MINUS sugar water, the amount of sugar water after subtraction is 30-20= 10 (kg).
(2) Sugar concentration
Formula:
Water before adding sugar, syrup after adding water.
If you subtract sugar water from sugar water, you can easily solve the problem.
Example: There is 20kg of sugar water with the concentration of 15%. How many kilograms of sugar are added, and the concentration becomes 20%.
Water needs to be added before sugar is added. The original water content is 20x (1-15%) =17 (kg).
When the water is exhausted, how much sugar water with a concentration of 20% should there be, including 17kg water,17/(1-20%) = 21.25 (kg).
Sugar water minus sugar water, the amount of sugar water minus the original amount of sugar water is 2 1.25-20= 1.25 (kg).
Fourth, the distance problem.
(1) encountered a problem.
Formula:
At the moment we met, the distance disappeared.
Divide by the sum of the speeds and you get the time.
Example: A and B walk in opposite directions from two places with a distance of 120km. Party A's speed is 40km/h and Party B's speed is 20 km/h. How long did they meet?
At the moment we met, the distance disappeared. That is, the distance traveled by Party A and Party B is exactly 120km.
Divide by the sum of the speeds and you get the time. That is, the total speed of Party A and Party B is 40+20=60 (km/h), so the meeting time is 120/60=2 (h).
(2) Traceability problem
Formula:
Slow birds fly first, fast birds chase after them.
The distance to go first, divided by the speed difference,
The time is right.
Brother and sister go to town from home. Big sister walks at a speed of 3 kilometers per hour. After walking for 2 hours, my little brother rode at a speed of 6 kilometers per hour. When will he catch up?
The distance to go first is 3X2=6 (km).
The speed difference is 6-3=3 (km/h).
So the catch-up time is: 6/3=2 (hours).
Primary school mathematics formula (3)
Verb (abbreviation of verb) and ratio problem
It is known that the whole is divided into parts.
Formula:
Family members want everyone to be together, and separation is also principled.
Denominator ratio sum, numerator's own.
And multiply by the ratio, you deserve it.
Example: The sum of the three numbers A, B and C is 27, A; B: C =2:3:4。 Find the numbers a, b and C. ..
The denominator ratio sum, that is, the denominator is: 2+3+4 = 9;
If the molecule is its own, then the proportions of A, B and C in the total are 2/9, 3/9 and 4/9 respectively.
And multiplication ratio, so the number a is 27X2/9=6, the number b is 27X3/9=9, and the number c is 27X4/9= 12.
Sixth, the difference ratio problem (difference multiple problem)
Formula:
I am more than you, and multiples are cause and effect.
Actual difference of numerator, multiple difference of denominator.
The quotient is double,
Multiplied by their respective multiples,
You can get two numbers.
For example, the number A is greater than the number B 12, and A: B = 7: 4. Find two numbers.
First, double the amount, 12/(7-4)=4,
So the number A is 4X7=28 and the number B is 4X4= 16.
Seven, engineering problems
Formula:
The total project amount is set to 1,
1 divided by time is work efficiency.
When a person does it, the work efficiency is his own.
When doing it together, the work efficiency is the sum of everyone's efficiency.
1 Subtract what has been done and what has not been done.
What is not completed divided by work efficiency is the result.
Example: A project will be completed in 4 days by yourself and 6 days by yourself. After Party A and Party B do it at the same time for 2 days, how many days will Party B do it alone? [1-(1/6+1/4) x2]/(1/6) =1(days)
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