"Fractional equations that can be converted into linear equations of one variable" PPT courseware

Description

"Fractional equations that can be converted into linear equations of one variable" PPT courseware

learning target

【teaching objectives】:

1. Become more proficient in solving fractional equations that can be converted into linear equations of one variable.

2. Cultivate students’ mathematical application awareness through applied teaching of fractional equations.

【main difficulty】:

Key points: Let students learn to examine the unknowns and formulate fractional equations.

Difficulty: Set up elemental fractional equations in different practical problems.

1. Review questions

What are the general steps for solving word problems using equations?

1) Review the meaning of the question clearly;

2). Assume unknown numbers;

3), list the expressions, find the equivalent relationship, and establish the equation;

4), list equations;

5) Check whether the solution of the equation conforms to the meaning of the question;

6), answer.

These problem-solving methods and steps are also applicable to learning fractional equation word problems. In this lesson, we will learn to solve word problems using fractional equations.

Application exploration of fractional equations

Solution to the problem introduced:

Solution: Suppose B can input the results of x students per minute, then A can input the results of 2x students per minute. According to the question,

Emphasis: It is necessary not only to check whether the solution sought is the solution of the original fractional equation, but also to check whether it conforms to the meaning of the question; the time must be unified.

2640/2x=2640/x-2×60

Solve to get x=11

After testing, x=11 is the solution of the original equation. And x=11, 2x=2×11=22, which is consistent with the meaning of the question.

Answer: A can input the results of 22 students per minute, and B can input the results of 11 students per minute.

3. Example explanation and practice

Example 2 A and B are 135 kilometers apart. Two cars are driving from A to B. The big car leaves 5 hours earlier than the small car, and the small car arrives 30 minutes later than the big car. The speeds of the small car and the big car are known. The ratio is 5:2. Find the speed of the two cars.

Analysis: It is known that the ratio of the speeds on both sides is 5:2, so assuming that the speed of the large car is 2x kilometers/hour, the speed of the small car is 5x kilometers/hour, and the distance between A and B is 135 kilometers, then The driving time of the big car is 135/2x hours, and the driving time of the small car is 135/5x hours. From the meaning of the question, we can know that the big car starts 5 hours earlier and arrives 30 minutes earlier than the small car. The actual driving time of the big car is 4.5 hours longer than the small car. This leads to the equivalent relationship

Solution: Suppose the speed of the big car is 2x kilometers/hour and the speed of the small car is 5x kilometers/hour. According to the question, we get

135/2-135/5x=5-1/2

The solution is x=9

After checking, x=9 is the solution of the original equation

When x=9, 2x=18, 5x=45

Answer: The speed of the big car is 18 km/h, and the speed of the small car is 45 km/h.

Learning summary

1. What knowledge have you learned? What should we pay attention to?

2. What experience did you have during the learning process?

Class summary

(1) What is the difference between solving word problems using a column of fractional equations and a column of linear equations of one variable?

(2) Can you summarize the steps for the following fractional equation word problems?

General steps for solving word problems using column fraction equations:

(1) Review the meaning of the question;

(2) Assume unknown numbers (must have units);

(3) List the formulas based on the quantitative relationships in the question, find the equality relationships, and list the equations;

(4) Solve the equation and check the roots, and check whether the solution of the equation conforms to the meaning of the question;

(5) Write the answer (must have units).

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"Fractional equations that can be converted into linear equations of one variable" PPT courseware 2:

"Fractional equations that can be transformed into linear equations of one variable" PPT courseware Learning objectives [Teaching objectives]: 1. Further become proficient in solving fractional equations that can be transformed into linear equations of one variable. 2. Cultivate students’ mathematical application awareness through applied teaching of fractional equations. [The key point is difficult...

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Update Time: 2024-10-02

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 1 industry PPT template

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