Able to solve equations and fractional equations, and the application problems of fractional equatio

Accurately find out the relationship between equal quantities, it is best to lay a good foundation, look at some example problems, and then do it yourself, and then compare your own practice with the work in the book, and do more questions, you will have the feeling of doing problems, and it will be easy to do any problems at that time.

Let's start by finding an equivalence relationship.

For example, find a b=c.

And then generally for fractional equations.

A or b, c often has a fraction.

Then it depends on how to put X inside A, B, and C.

Let's take a simple example.

1000 yuan is used to purchase books, and after the price is reduced by 5 yuan, you can buy 10 more books than the original, so how much is the original price?

If the original price is x, the equivalent relationship can be listed.

The original number is 10 = the current number.

Then it can be clearly known.

Original number = 1000 x

Number of present copies = 1000 (x-5).

Then the equation naturally comes out.

1000/x 10=1000/(x-5)

Grasp the relationship between several quantities of travel problems.

Distance = Speed * Time; Speed = distance time; Time = distance No matter how the speed changes, it is inseparable from these quantitative relationships.

To do more of this type of question, first look at the example questions, and then practice on your own, and gradually get started. The key to doing this kind of application problem is to find the equivalent relation, and after finding it, it is expressed in known quantities and unknown quantities, and it is listed.

An equation with a fraction and an unknown number in the denominator – a fractional equation.

Productivity: Working hours, Total amount of work.

Total amount of work, work efficiency, working hours.

Total work, working hours, work efficiency.

Factor Factor product.

The product of one factor is another factor.

Column Fractional Equation Solving Practical Problems:

1) Steps: Review the problem - set the unknown number - column equation - solve the equation - test - write the answer, pay attention to the test from the equation itself and the actual problem when testing.

2) basic types of application questions;

a.Itinerary problem: The basic formula: distance = speed and time and the itinerary problem is divided into encounter problem and chase problem.

b.Numerical Problems In numerical problems, it is necessary to master the notation of decimal numbers.

c.Engineering Problems Basic Formula: Workload = Man-hours Ergonomics.

d.Backward water problem v Backward water = v static water + v water v reverse water = v still water - v water.

Math fractional equations are similar to solving fractional equations.

First of all, for the word problem, you have to list the equation according to the question conditions.

Then there's the problem of solving the equations.

The basic steps for solving fractional equations are as follows.

1. Find the value range of the unknown number x first, this is very important, then you will know that you need to find the definition domain of the function first when you go to high school, such as the denominator can not be 0 or the like, and the specific situation will be analyzed on a case-by-case basis.

2. Remove the denominator, eliminate the unknowns in the fraction, convert them into general equations, and then solve them according to the method of solving general equations.

3. The last step is the test, you have to test the x value you are looking for to see if it meets the requirements of the original topic, whether it meets the actual situation, and whether it meets the equation in the equation.

1.Solution: Set the excess part of the water fee of x yuan per cubic meter, according to the topic (

solution, get x=2

Answer: The excess part will be charged 2 yuan per cubic meter of water.

2.Solution: Set the purchase price of the commodity to be Y yuan, according to the topic.

6000÷【y（1+20%）-y】=（6000+2000）÷【y（1+10%）-y】-100

solution, get y=500

Then, the total number of pieces sold in the mall in the second month is: (6000+2000) [500 (1+10%)-500] = 160 (pieces).

Answer: The purchase price of the goods is 500 yuan, and the mall sells a total of 160 pieces in the second month.

Hey, Magic Bubble Kyt, me want to be the best.

Zhang's household ** water 10 yuan.

Li household ** water 20 yuan.

Set ** water per cubic meter x yuan.

10 x + 5 = 2 3 (20 x + 5) is solved to get x = 2 yuan.

Solution: Let the specified date be x days From the meaning of the question, 3x+xx+6=1 (3 points) The solution is: x=6

Tested: x=6 is the root of the original equation (5 points).

Clearly, option (2) does not meet the requirements;

Scheme (1): 10,000 yuan);

Plan (3): 10,000 yuan).

Because, on the premise of not delaying the construction period, choose the third construction plan to save the project money (8 points) The key descriptor is: "A and B teams work together for 3 days, and the rest of the project is completed on schedule by team B alone"; It shows that team A actually worked for 3 days, and team B worked for x days to complete the task, and the workload = working time The equivalent relationship between work efficiency is: 3 days of work of A + work of B on the specified day = 1 column of equations

Look at the cost again: scheme (1) and (3) do not delay the construction period, meet the requirements, and can ask for the cost, and scheme (2) obviously does not meet the requirements

Solution: If the specified construction period is x days, then A can be completed in x days, and B needs x + 6 days to complete, and the total amount of work is 1, then there is an equation;

1-3[1/x+1/(x+6)]}x+6)=x-31-(6x+18)/x(x+6)]=x-3)/(x+6)x²-18)/x(x+6)=(x-3)/(x+6)x²-18=x(x-3)=x²-3x

3x=18, so x=6 days.

That is, the stipulated completion time is 6 days.

Therefore, the plan requires a project cost of 10,000 yuan); The plan requires 10,000 yuan for the project) [delay the construction period of 6 days]; The project needs to be paid (10,000 yuan).

Therefore, under the condition of ensuring that the project is completed on schedule, the first plan is preferred.

How to understand the problem of fractional equations:

1. Review the topic.

Two: Correctly set the unknowns.

Three: Find the equal amount in the question.

4. Solve fractional equations.

Five: inspection (1.)See if the value of the solution is the solution of the original fractional equation; 2.See if it meets the topic, and if it doesn't, you have to discard it).

Six: Answer. Hope it helps!

Good luck with your studies!

Steps to solve a problem with column fractional equations:

1. Review the problem and find the relationship between the same amounts;

2. Set unknowns;

3. a column equation;

4. Transform into an integer equation;

5. Solving integer equations;

6. Inspection; 7. Answer.

The twofold meaning of the test:

1) Check that it is a solution to the listed fractional equation; (2) Check whether it is a solution to the problem.