"Applications of Fractional Equations" PPT Courseware 2

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"Applications of Fractional Equations" PPT Courseware 2

Example: A and B make certain machine parts. It is known that A makes 6 more parts per hour than B. The time it takes A to make 90 parts is equal to the time it takes B to make 60 parts. Find the parts of A and B per hour. How many parts are made?

Equivalent relationship: A’s time = B’s time

Solution: Suppose A makes x parts per hour, then B makes (x-6) parts per hour. According to the meaning of the question, we get

90/x=60/x-6

90(x-6)=60x

Solving this equation, we get

x=18

After testing, X=18 is the root of the original fraction equation and conforms to the meaning of the question.

From x=18, we get x-6=12

Answer: A does 18 reps per hour, B does 12 reps per hour

General steps for solving word problems using column fraction equations

1. Suppose: Analyze the meaning of the question and find out the quantitative relationship. Use letters to represent an unknown number in the question.

2. Find: Find an equality relationship that can express the full meaning of the word problem

3. Column: Correctly list fractional equations based on quantities and equality relationships.

4. Solution: Solve this fractional equation carefully.

5. Verification: Check. (Whether it is the root of the fractional equation, whether it conforms to the meaning of the question)

6. Answer: Pay attention to the completeness of the units and language.

Example question analysis:

Two engineering teams jointly participated in a road construction project. Team A worked alone for one month to complete one third of the total project. At this time, Team B was added. The two teams worked together for another half a month, and the total project was completed.

Which team has the fastest construction speed?

Team A completes _____ of the total project in one month. Suppose Team B completes _____ of the total project in one month. Then Team A completes _____ of the total project in half a month, and Team B completes _____ of the total project in half a month. _____, the two teams completed the total project in half a month.

What is the key to making equations? Which equivalence relationship in the problem can be used to formulate an equation?

The workload of Team A for one month of construction + the workload of Team A and B for half a month of construction = total workload

Choose one

Class A and Class B are participating in campus tree planting activities. It is known that Class A plants 10 more trees every day than Class B. The number of days it takes Class A to plant 100 trees is equal to the number of days it takes Class B to plant 80 trees. If Class B plants x trees every day, the equation according to the question is ( )

A. 100/x-10=80/x ​​B. 100/x=80/x+5

C. 100/x+10=80/x ​​D. 100/x=80/x-5

4. Places A and B are 135 kilometers apart. There are two cars, a big one and a small one, 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.

It is known that the ratio of the speeds of the large and small cars is 2:5, find the speeds of the two cars.

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

135/2x-4.5=135/5x

Please complete the process below

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For more information about the "Applications of Fractional Equations" PPT courseware, please click on the "Applications of Fractional Equations" ppt tab.

"Applications of Fractional Equations" PPT courseware 3:

"Applications of Fractional Equations" PPT Courseware 3 Review Review 1. Concept of fractional equations An equation containing an unknown number in the denominator is called a fractional equation. 2. Problem-solving ideas for solving fractional equations 3. Problem-solving steps for solving fractional equations Learning objectives: 1. Be able to analyze the meaning of the problem and find equivalent quantities..

"Applications of Fractional Equations" PPT courseware:

Summary of the "Applications of Fractional Equations" PPT courseware: Steps and methods for solving application problems with column fraction equations: 1. Review, set up, list, solve, test, and answer 2. Find equivalent relationships Summary Summary of solving column fraction equations General steps and precautions for application questions: (1) Question review:..

"Applications of Fractional Equations" Fraction PPT Courseware 2:

"Applications of Fractional Equations" Fractional PPT courseware 2 Teaching objectives: 1. Use the list method to list fractional equations and solve problems in real situations. 2. Understand the application value of mathematical models. Teaching focus: Use the list method to clarify the meaning of the question and convert practical problems into fractional equations.

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Update Time: 2024-11-30

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

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