How to find the equivalence relation, eight ways to find the equivalence relation

In fact, the key to solving the problem is to find the equiquantity relationship, find the equiquantity relationship, and the equation can be listed So how to find the equiquantity relation? (1) Grasp the mathematical terminology to find the equivalent relationship The quantitative relationship in the application problem: the general sum difference relationship or multiple relationship, often used "altogether", "ratio......more", "than ......Less", "Yes......When solving the problem, you can grasp these terms to find the equivalence relationship and list the equations in the order of description, for example:

The school carried out tree planting activities, and 50 trees were planted in the fifth grade, which is 4 trees less than twice the number of trees planted in the fourth grade. The key word in this question is "...... comparison."less", from here we can find this equivalent relation: 2 times the number of trees planted in the fourth grade minus 4 is equal to the number of trees planted in the fifth grade, from which the equation 2 4 50 (2) finds the equivalence relation according to the common quantity relation Common quantity relation:

Work efficiency Working hours Total amount of work; Unit price, quantity, total price; The speed of the time of the distance ......For example: "The retail price of a certain style of clothing is 36 yuan for 1 set, and the existing price is 216 yuan, how many sets of clothes can I buy in total?" According to the quantitative relationship of "unit price, quantity, total price", equation 36 216 crying is.

There's no need to look for this, just do the math.

Eight ways to find equations in a series of equations with equal quantities.

First, start with the key sentence to find the equivalence relationship.

The key sentence is the core of the quantitative relationship reflected in the application problem. Before solving the problem, we should carefully review the problem, find out the key sentences from the question, and then express the key sentences in the language and text equation, so as to list the equation For example: there are 38 girls in a class, 4 times more than the number of boys, how many boys, replace the key sentence "4 times more than the number of boys" with the number of girls, the number of boys 2, 4 or the number of girls, 4, the number of boys 2 can get the equation 2x+4=38 2x=38-4 respectively.

Second, with the help of the basic equiquantitative relation series of equations.

Before learning the equation problem, you should memorize "speed, time, distance, unit price, quantity, total price, work efficiency, working time, workload, total quantity?" Total number of copies, average.

and other basic quantitative relationships. The equations are presented by analyzing the relationship between the three through these basic quantitative relationships.

3. Column equations according to the calculation formula:

We have mastered some calculation formulas in the study of basic knowledge of geometry, and these formulas are a kind of equiquantitative relationship. For example: parallelogram area, triangle area.

Trapezoidal area, circular area formula.

Fourth, draw a line segment diagram to find the equivalent relationship:

A standardized line diagram clearly and intuitively reproduces the quantitative relationship of the problem, from which the equivalent relationship can be found.

5. Use the computational properties to find the equivalence relationship

In the four calculations, we have learned the properties of the laws of arithmetic, which essentially embody an equivalence relation, according to which we can list equations, such as dividing a number by 9 quotients and 7 remainders by 5, which is divided by 10 quotients and 6 remainders, according to the "dividend."

Quotient divisor, remainder.

The equation is: 10 6+x=9 7+5

6. Find the equivalent relationship according to the geometric characteristics.

Special geometries have certain characteristics based on which we can find equiquantitative relations and list equations, such as an isosceles triangle.

The apex angle is 40 degrees, and an isosceles triangle has the characteristic that two base angles are equal, so that the equivalence relationship is obtained: the degree of a base angle 2, the degree of the apex angle, 180 degrees, and the equation can be obtained: 2x+40=180.

7. Find an equal relationship from the facts described in the title.

There are a lot of narrative problems, and you can read them and refine them into textual equations, and list equations according to the meaning of the questions, for example, the store originally had 74 kilograms of fruit candy, and another 25 kilograms were shipped, and after selling it for a day, there were 63 kilograms left. How many kilograms were sold on this day, and while reading and refining, it was refined as: the original, the shipped, the sold, and the rest of the equation:

8. Find the relationship between the same quantity according to the "same quantity".

For example, a car from A to B plans to travel 35 kilometers per hour and arrives in 6 hours, and actually arrives 2 hours in advance, although the time and speed in the question have changed, but the planned and actual distances are the distances between A and B, that is, the planned distances and the actual distances traveled are the distances between A and B, that is, the planned distances, the actual distances traveled, so the equation can be obtained: (6-2)x=35 6

Ideas for solving problems in junior high school math application problems, looking for equiquantitative relationships.

Equiquantitative relationsEquiquantity relation" is a kind of quantitative relation. Mathematics problems often contain a variety of equivalence relationships, for example, when using equations to solve application problems, it is necessary to find the equivalence relationship of Sun Yin in the problem.

Common methods1. Grasp the key mathematical terms to find the equivalence relationship.

Quantitative relations in practical problems: general and difference relations or multiples relations, often used "altogether", "ratio......more", "than ......Less", "Yes......several times" and other terms. When solving the problem, you can grasp these terms to find the equivalence relationship and list the equations in the order of description.

2. Find the equivalent relationship according to the common quantity relationship.

A common quantity relationship: productivity.

Working hours Total amount of work; Unit price, quantity, total price; speed, time, distance, and so on.

3. Find the equivalent relationship according to the commonly used calculation formula.

A commonly used formula is the area formula for geometric figures.

There are: rectangular area, length and width; The area of the triangle.

1 2 (the bottom is high and buried Kaimeng); Quadrilateral area of parallel curved bridge = base height.

4. Draw a line segment diagram to find an equal relationship.

For example: "If a farm has 400 hectares of wheat, 70 hectares of wheat are harvested every day for the first three days, and the rest is harvested in 2 days, how many hectares of wheat is harvested per day on average?" "Draw a line diagram according to the theme first.

From the line diagram, it can be intuitively seen: the total number of wheat cuts, the number of wheat harvested in the first 3 days, and the number of wheat harvested in the next 2 days. According to this relation, equation 70 3 2x 400 can be listed.

When we are doing problems, as long as we think carefully and analyze, there will always be some unexpected gains. Here are a few ways I found how to find the equivalence relationship when I was doing math problems: 1. Grasp the key sentence to find the equation of the equivalence relationship For example:

On Sunday, my mother went to the street to buy some fruits, and my mother bought 3 watermelons, and the number of apples she bought was 3 times more than 1 watermelon, how many watermelons were there? The key sentence of this question is: the number of apples is 3 times more than 1 watermelon, from which we can find out the quantity relationship Watermelon 3-1 = the number of apples, let the number of watermelons be , you can list the equation as:

3 -1=3 2. Column equations according to the relevant geometric formulas For example, the height of a triangle is 5 decimeters.

The area of the triangle is 50 square decimeters, what is the base of the triangle in decimeters? According to the area formula of the triangle triangle area.

Bottom height 2 "Let the base of the triangle be decimeters, and you can list the equation 5 2=50 3. Find the equation of the equivalence off series according to life experience For example: I have 10 pieces of sugar, and after eating a few pieces, I bought 4 pieces, and now I have 11 pieces of sugar, how many pieces do I eat? We know that the original number of sugars - the number of sugars eaten + the number of sugars bought again = the number of sugars now.

According to this equiquantitative relationship, it is easy to list the equation if you eat a lump of sugar: 10- +4=11 In life we can find mathematics, because mathematics is closely related to our lives, as long as you are a child who is willing to observe, you will definitely find fun in the kingdom of mathematics. Sihong County Weiying Town Central Primary School Zhang Jujie Fushi.

1. Find the equivalent relationship according to the commonly used calculation formula:

Commonly used quantitative relations: rectangle area, length, width; For example: "The area of a rectangle is 19 square meters, and its length is 4 meters, so how many meters is the width?"

According to the formula for calculating the area of a rectangle, "Length, Width, Area", equation 4 19 can be listed.

2. Master mathematical terminology to find equivalence:

Common quantitative relations: general and difference relations or multiple relations, commonly used "altogether", "than? Many", "Sleepy than? Less", "Yes......When solving the problem, you can grasp these terms to find the equivalence relationship and list the equations in the order of description.

3. Find the equivalent relationship according to the common quantity relationship

Common quantity relationships: work efficiency, working hours, total work; Unit price, quantity, total price; The speed of the time of the distance ......When solving the cherry tree ruler trace, you can find the equivalent relationship according to these quantitative relationships.

4. Determine the equiquantity relationship with the help of line segment ridge and diagram.

The line diagram can make the abstract quantitative relationship concrete, and make the hidden quantitative relationship clear. For more complex questions, students can use line diagrams to find equivalence relationships.

5. Find the equivalent relationship according to the text relation.