First, correctly finding the unit "1" is the premise to solve the problem of score application.

No matter what kind of fractional application problem it is, there must be a unit "1" in the problem. Finding the unit "1" correctly is the premise and primary task to solve the problem of fractional application.

The unit "1" in the problem of fractional application appears in two forms:

1, clearly marked:

(1) The number of boys accounts for 4/7 of the class. (2) Poplar is 3/5 of willow. (3) Xiaoming's weight is 1/2 of his father's. (4) There are more apple trees than pear trees 1/5.

Among the conditions of "accounting", "yes" and "equivalent", the quantity before the score is the unit "1" in this question.

2. No obvious signs:

(1) A road has been repaired for 200 meters, and 2/3 of it has not been repaired. How many kilometers is this road?

(2) 200 sheets of paper, first use 1/4, second use 1/5. Two * *, how many were used? (3) The typist typed a 5000-word manuscript and typed 3/ 10. How many words are left?

The unit "1" in these three questions has no obvious mark, so it should be judged comprehensively according to the questions and conditions. In (1), "the total length of a road" should be regarded as the unit "1"; (2) "200 sheets of paper" shall be regarded as the unit "1"; (3) "5000 words" should be regarded as the unit "1".

Second, finding the correct correspondence is the key to solving the problem of fractional application.

Every fractional application problem has a corresponding relationship between quantity and fraction, and correctly finding out which fraction (or quantity) corresponds to the required quantity (or fraction) is the key to solving fractional application problems.

1, draw a line segment to find the corresponding relationship.

(1) There are 12 ducks and 4 geese in the pond. What is the number of geese? (2) There are 12 ducks in the pond, and the number of geese is 1/3 of that of ducks. How many geese are there in the pond? (3) There are four geese in the pond, which is exactly 1/3 of the number of ducks. How many ducks are there in the pond?

Show the relationship between these three problems with a line chart. As can be seen from the figure, drawing a line segment diagram is an effective means to find the corresponding relationship correctly. Line drawing can help students understand the quantitative relationship, and at the same time can draw the following quantitative relationship:

Number corresponding to score ÷ number of units "1" = number of units "1"× number corresponding to score ÷ number of units "1"

2. Find the corresponding relationship from the conditions in the question.

A bucket of water is 1/4, which is exactly 10g. How much does this bucket of water weigh? 3/4 of water =10

Thirdly, according to the quantitative relationship, the "three-step method" is adopted to solve the problem of score application.

Mastering the above relationship and quantity relationship, solving the application problem of fractions can be carried out in the following three steps: 1, and finding the quantity of the unit "1"; 2. Identify the correspondence 3. Solve problems according to quantitative relations.

Fourth, practice effectively, build a model and improve the ability to solve fractional application problems.

In order to solve the problem of fractional application correctly and quickly, we must practice more and understand the basic, slightly complicated and complicated structural features clearly, so as to solve the problem of fractional application skillfully and quickly.

basic theory

(A) the construction of fractional application problems

1, fractional application problem is the key and difficult point in primary school mathematics teaching. It can be roughly divided into two types:

(1) The basic quantitative relationship is basically the same as the integer application problem, except that the known number in the integer application problem is changed to the component number and solved.

The answer method is basically the same as the integer application problem.

(2) Fractional application problem with unique solution based on the meaning of fractional multiplication and division, which is what we usually call it.

Fraction application problem.

2. Fractional application questions mainly discuss the relationship between the following three:

(1) score: a score indicating that one number is another number, usually called a score.

(2) Standard quantity: When solving a fractional application problem, the number in the problem as the unit "1" is usually called standard quantity. (3) Comparison quantity: When solving fractional application problems, the number compared with the standard quantity in the problem is usually called comparison quantity. (B) the classification of the application of scores

1, find the fraction of a number. The characteristic of this kind of problem is to know that a number is regarded as the unit "1", find its score, and solve this kind of application problem by multiplication. That is, the application problem that reflects the relationship between the whole and the part. The basic quantitative relationship is: total quantity × score = number of parts corresponding to score; Or know a number whose unit is "1" and another number accounts for its fraction, and find another number, that is, an application problem that reflects the relationship between two numbers. The basic quantitative relationship is: standard quantity × score = comparative quantity corresponding to score.

2. Find the fraction of one number to another. The characteristic of this kind of problem is to know two quantities and then compare them.

Multiple relations, division is used to solve this kind of application problems. The basic quantitative relationship is: comparison quantity ÷ standard quantity = score.

(1) Find the score of one number to another: comparison quantity ÷ standard quantity = score (score). (2) Find how many fractions one number is more than another: difference ÷ standard quantity = fraction (how many fractions). (3) Find how many fractions one number is less than another number: difference ÷ standard quantity = fraction (how many fractions are less).

3. Find the score of a given number. The characteristic of this kind of problem is to know the fraction of a number, find the unit "1", and solve this kind of application problem by division. The basic quantitative relationship is: the comparative quantity corresponding to the score ratio = the standard quantity.

Hope to adopt