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

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

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), solve 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,

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 1: 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. It is known that the distance between the small car and the big car is The ratio of the speeds is 5:2. Find the speeds of the two cars.

Example 2: A worker originally planned to produce 840 parts within a certain number of days. He continued production according to the original plan for the first 4 days. After that, the number of parts produced every day increased by 25% compared with the original plan. As a result, the task was completed 2 days ahead of schedule. How many days did it take to complete the original plan? Task?

Example 3: Two people A and B set out from places A and B, which are 36km apart, and walked towards each other. When A set out from place A and reached 1km, he found that the forgotten items were at place A, so he immediately returned, took the items and immediately returned from A walks towards B, so that A and B meet exactly at the midpoint of AB. We also know that A travels 0.5km more per hour than B. Find the speed of A and B?

Example 4: Two teachers took several students on a trip and contacted two travel companies, A and B. The preferential conditions given by company A were: 1 teacher was charged the full fare according to the unified regulations of the industry, and the rest were charged at a 25% discount; B The preferential conditions given by the company are: all charges are 20% off. After calculation, company A’s preferential price is cheaper than company B’s preferential price. How many students will participate in the tour?

practice

(1) Two people A and B start from A at the same time and ride bicycles to B. It is known that the distance between AB and AB is 14km. A's speed is 3 times that of B, and he arrives 40 minutes before B. How far do A and B each walk per hour?

(2) A group of students took a bus for a spring outing. It was estimated that the total fare was 120 yuan. Later, the number of students increased by 1/4, and the cost remained the same. In this way, each person would pay 3 yuan less. How many students were in this group?

(3) A certain project is completed within a time limit. If Team A does it alone, it will be completed on time, but if Team B does it alone, it will be delayed by 3 days. After the two teams cooperate for 2 days, the remaining projects will be done by Team B alone, and it will be completed on time. What is the deadline of the project? how many days?

(4) A, B, and C cooperate to complete a project in 12 days. It is known that A completes the work in one day, B needs 1.5 days, and C needs 2 days. Find the number of days it takes three people to complete the project alone.

(5) Xiao Ming and Xiao Liang typed a manuscript together. After 4 hours, Xiao Ming had other tasks, so Xiao Liang completed the remaining work alone. After another 5 hours, the task was completed, which was faster than originally scheduled (two people completed it together). ) is delayed by 1 hour. Ask Xiao Ming, how long will it take Xiao Liang to complete this task alone?

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:

"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: 2024-11-18

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

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