"Fractional Equations" Fractional PPT

Description

"Fractional Equations" Fractional PPT

Part One: Knowledge Review

1. Observe, what equation is this?

linear equation of one variable

2. What are the characteristics of a linear equation of one variable?

① Contains only one unknown number

②The degree of the unknown is 1

③Every item is an integer

3. What are the steps to solve a linear equation of one variable?

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?

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

The speed along the current is ________ kilometers/hour;

The speed against the water is ________ kilometers/hour;

According to the meaning of the question, we have

Fractional equation PPT, part 2 content: content analysis

Fractional equation

Which of the following equations are fractional equations? Which integral equations.

Explore

Let's study together how to solve fractional equations:

Multiply both sides of the equation by (30+v) (30-v) to get:

Solving Fractional Equations

Solution: Multiply both sides of the equation by the simplest common denominator (x-5) (x+5) to get:

x+5=10

Solution: x=5

test:

Substituting x=5 into x-5, the values ​​of x-25 are both 0, and the corresponding fractions are meaningless.

So x=5 is not a solution to the original fraction equation.

∴The original fractional equation has no solution.

Increase roots

Definition of rooting

Augmented root: A root that is solved by removing the denominator from the integer equation so that the denominator is zero.

Root augmentation meets two requirements:

① is the root of the corresponding ______ equation.

②Make the _______ of the fractional equation be 0.

How to check

How to check whether the solution of the obtained integral equation is the solution of the original fractional equation?

Substituting the solution of the integral equation into the simplest common denominator,

If the value of the simplest common denominator is not 0,

Then the solution of the integral equation is the solution of the original fractional equation,

Otherwise, this solution is not the solution of the original fractional equation.

Fractional Equations PPT, Part 3: Summary

What did we learn in this lesson?

1. Ideas for solving fractional equations:

2. General steps for solving fractional equations:

①Remove the denominator

②Solve integral equations

③Inspection

Note: Inspection is essential.

1. Solution to fractional equations containing parameters: Treat the parameters as known numbers and solve them normally.

2. It is known that the equation has steps to add roots and find parameters:

① Treat the parameters as known numbers and solve the fractional equation

② Then based on the denominator being 0, an equation about the parameters is obtained.

③ Solve the parameters.

Keywords: Free download of PPT courseware for eighth-grade mathematics from the People's Education Press, PPT download of fractional equations, PPT download of fractions, .PPT format;

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

"Fractional Equations" Fractions and Fractional Equations PPT (Lesson 3):

"Fractional Equations" Fractions and Fractional Equations PPT (Lesson 3), 26 pages in total. Learning objectives: Be able to express equality relationships in practical problems using fractional equations. Master the method of solving practical problems using fractional equations. ... ... ... Activity exploration Exploration point 1 Question 1:..

"Fractional Equations" Fractions and Fractional Equations PPT (Lesson 2):

"Fractional Equations" Fractions and Fractional Equations PPT (Lesson 2), 22 pages in total. Learning objectives: Master the basic ideas and solutions of fractional equations. Understand the reasons why fractional equations may have increased roots, and master the method of checking the roots of fractional equations. ... ... ... Activity exploration Explore...

"Fractional Equations" Fractions and Fractional Equations PPT (Lesson 1):

"Fractional Equations" Fractions and Fractional Equations PPT (Lesson 1), 21 pages in total. Learning objectives: Understand the meaning of fractional equations. Be able to analyze practical problems and formulate fractional equations according to the meaning of the questions. ... ... Activity exploration Exploration point 1 Question 1: A and B are 1400km apart,...

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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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