"Fractional Equations" Fractional PPT (Fractional Equations and their Solutions in Lesson 1)

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"Fractional Equations" Fractional PPT (Fractional Equations and their Solutions in Lesson 1)

Part One: Problem Situation

The maximum speed of a ship in still water is 30 kilometers per hour. The time it takes for it to sail 90 kilometers downstream at its maximum speed is equal to the time it takes to sail 60 kilometers upstream at its maximum speed. What is the flow speed of the river?

Analysis: Suppose the flow speed of the river is v kilometers/hour, then

The ship sails downstream at a speed of ______ kilometers/hour,

The speed of sailing against the current is ______ kilometers/hour,

The time it takes to sail 100 kilometers downstream is ______ hours,

The time it takes to sail 60 kilometers against the current is ______ hours.:

Fractional Equations PPT, Part 2: Introducing New Knowledge

The concept of fractional equation: An equation containing unknown numbers in the denominator is called a fractional equation.

Follow-up question: Can you write a few more fractional equations?

The equations we have studied before are all integral equations, and their unknowns are not in the denominator.

Fractional Equations PPT, Part 3: Consolidation Practice

Exercise 1 Which of the following are fractional equations?

Thinking: How to solve fractional equations ①

You can first remove the denominator and convert the fractional equation into the well-known integral equation, and then solve the integral equation.

In conclusion

What are the key steps to convert equation ① into an integral equation?

The basic idea of ​​solving fractional equations ① is to convert the fractional equation into an integer equation. The specific method is to "remove the denominator", that is, multiply both sides of the equation by the simplest common denominator. This is also a general method for solving fractional equations.

Exercise 2 Point out the simplest denominator of each denominator in the following equations, and write the integral equation obtained after removing the denominator.

Is x=5 the solution of the original fraction equation?

Substituting x=5 into the original fraction equation to test, it is found that the values ​​of the denominators x-5 and x2-25 are both 0, and the corresponding fractions are meaningless. Therefore, although x=5 is the solution to the integral equation x+5=10, it is not the solution to the original fractional equation. In fact, this fractional equation has no solution.

Fractional Equations PPT, Part 4: Practice in class

1. Multiply both sides of the fraction equation by x-1, and after removing the denominator, we get ( )

A.2-(2-x)=1

B.2+(2-x)=1

C.2-(2-x)=x-1

D.2+（2－x）=x－1

Fractional Equations PPT, Part 5: Class Summary

General steps for solving fractional equations:

Fractional equation Integral equation

x=a

x=a is the solution to the fractional equation

x=a is not a solution to the fractional equation

One solution, two solutions and three tests

1. Multiply both sides of the equation by the simplest common denominator (be sure not to miss out on multiplying the integer of the original fraction equation), remove the denominator (the numerator is a polynomial, be sure to add parentheses), and turn it into an integer equation.

2. Solve this integral equation.

3. Substitute the solution of the integral equation into the simplest common denominator. If the value of the simplest common denominator is not 0, the interpretation of the integral equation is the solution of the original fraction equation; otherwise, this solution is not the solution of the original fraction equation and must be discarded. go.

4. Write the solution to the original fraction equation.

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For more information about the "Fractional Equations Fractional Equations and Their Solutions" PPT courseware, please click the Fractional Equations PPT Fractions PPT Fractional Equations and their Solutions PPT tab.

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Update Time: 2024-10-02

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

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