"Fractional Equations" Fractional PPT Courseware 2

Description

"Fractional Equations" Fractional PPT Courseware 2

teaching objectives

【Course Standards】

1. Understand the concept of fractional equations and the reasons for increasing roots.

2. Master the solution method of fractional equations, be able to solve fractional equations that can be converted into linear equations of one variable, and be able to test whether a number is an increased root of the original equation.

3. Be able to analyze the meaning of the question and find the equivalent relationship.

4. Fractional equations that can be converted into linear equations of one variable will be listed to solve practical problems.

【Knowledge and Ability】

Experience the process of "actual problems - fractional equation model - solve fractional equations - test rationality", develop the ability to analyze and solve problems, and cultivate application awareness.

[Emotional attitudes and values]

By learning classroom knowledge, students can understand that everything is interconnected, theory comes from practice, and they can use the knowledge they have learned to serve our lives.

General steps for solving fractional equations:

1. Multiply both sides of the equation by the simplest common denominator of each denominator, and remove the denominators to convert the fractional equation into a linear equation of one variable;

2. Solve this linear equation of one variable;

3. To test, substitute the obtained solution of the linear equation of one variable into the left and right sides of the original equation.

(1) The school is holding a rope skipping competition, and the students are practicing actively. The time it takes for student A to dance 180 times, student B can dance 216 times. It is also known that student A dances 20 fewer dances per minute than student B. How many dances does each person jump per minute?

Solution: Suppose A jumps x times per minute and write the equation, we get

180/x=216/x+20

Solution, we get x=100

After testing, x=100 is the root of the original fraction equation.

So B jumps x+20=100+20=120 (pieces) per minute

Answer: A jumps 100 times per minute, and B jumps 120 times per minute.

(2) A project must be completed within a deadline. If the first group works alone, it will be completed by the specified date; if the second group works alone, it will take 4 days beyond the specified date to complete. If the two groups work together for 3 days, the remaining work will be completed by the second group alone, exactly within the specified date. It must be completed within the specified date. How many days is the specified date?

Solution: Assume that the specified date is x day, and write the equation, we get

3(1/x+1/x+4)+x-3/x+4=1

Solution, we get x=12

After testing, x=12 is the root of the original fraction equation.

Answer: The specified date is 12 days.

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For more information about the PPT courseware "Fractional Equations and Fractions", please click the Fractional Equations ppt Fractions ppt tag.

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"Applications of Fractional Equations" PPT courseware 2:

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Update Time: 2024-07-01

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 1 industry PPT template

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