(1) A fraction with a denominator of 100 is called a percentage. This definition focuses on form and regards percentage as a special form of fraction.

(2) A number indicating that one number (comparison number) is a percentage of another number (standard number) is called a percentage. This definition focuses on application and is used to represent the ratio of two numbers. So percentage is also called percentage or percentage.

Percentages are usually not expressed in the form of fractions, but by the symbol "%",which is called the percent sign.

In the second definition, there are comparison number, standard number and score (percentage), and the relationship between them is as follows:

Contrast number/standard number = score (percentage), standard number × score = contrast number, contrast number/score = standard number.

According to the relationship between comparison number, standard number and score, many application problems related to percentage can be solved.

A number indicating that one number is a percentage of another. Percentages are also called percentages or percentages. Percentages are usually not written in the form of fractions, but are represented by the symbol "%"(called percent sign). For example, write 4 1% and 1% respectively. Since the denominator of the percentage is 100, it is all 65438+.

The formation of the concept of percentage should be based on students' real life or examples in industrial and agricultural production. For example, there are 100 students in senior one, among whom 47 are girls, accounting for 47% of the whole grade and 47% of the writing. For example, there are 200 senior two students, including girls 100, accounting for 50% of the whole grade. The number of students in two grades is "standard quantity", while the number of girls is "comparative quantity". In the teaching of percentage application problems, we should grasp the quantitative relationship = percentage (percentage) for analysis.

There are three calculation problems in the application of percentage: ① Find the percentage of one number to another, for example, find the percentage of 45 to 225, that is, = 20%; ② Find the percentage of a number; For example, find 75% of 2.2, that is, 2.2× 75% =1.65; 3 know one.

The knowledge of fraction and percentage is widely used in daily life and production construction, and it is also an important content of primary school mathematics. How to improve and strengthen the teaching of the application of fractions and percentages, so that they can properly reflect the practical application, so as to stimulate students' interest in learning, enhance the purpose and practicability of learning, and really improve the teaching quality, it is important to conscientiously implement the requirements of the teaching syllabus.

The new syllabus stipulates four application problems, including engineering problems; The practical application of percentage includes the calculation of germination rate, qualified rate and interest. , no more than three steps, limited to relatively easy calculation. This makes specific restrictions on the content and difficulty, which is conducive to ensuring the implementation of basic knowledge and problem-solving ability, preventing arbitrary high demands, artificially fabricating many unrealistic problems, and increasing students' learning burden.

First of all, I can answer questions about the application of fractions and percentages.

Being able to solve the requirements of fractional and percentage application problems generally means being able to understand the meaning of application problems, master the most basic quantitative relationship, correctly judge the calculation method, be able to calculate continuously, and be good at checking the rationality and accuracy of the solution.

Because of the quantitative relationship between fractions and percentage application problems, compared with integer application problems, it has both * * * and particularity, which requires students to understand both its * * * and its particularity, so as to improve their cognitive level. In this regard, a few examples are given below.

1. Fraction addition and subtraction application problem

There are two kinds of known fractions in the application of fractional addition and subtraction: one is to represent a specific quantity, and the other is to represent the ratio of two quantities. For example:

(1) The canteen burns tons of coal on the first day, tons of coal on the second day, and how many tons of coal are burned in two days? The known scores in the questions all represent specific quantities, which are consistent with the quantitative relationship with the application questions on integers. Ask students to know that this is the sum of two quantities in the same unit.

(2) There was a batch of coal in the canteen, which was burned on the first day and the next day. How much was burned in two days? The known score in the problem is the ratio of two quantities, not a specific quantity. Although the quantitative relationship conforms to the application problem of integer summation, it is * * *; But students should understand that the sum in the question is for this batch of coal, not the specific quantity.

(3) The surface area of the earth is ocean, and the rest is land, which accounts for a fraction of the surface area of the earth? The quantitative relationship of this problem is consistent with the calculation of the remainder in an integer by subtraction, which is * * *, but only one known condition is given in the problem. Another condition is that students should imagine the whole earth surface area as "1" and then use 1-=, which is different from the integer application problem.

2. Fraction, percentage multiplication and division application problems

The application problem of fractional multiplication and division not only contains the quantitative relationship of integer multiplication and division, but also has new quantitative relationship, which needs students to distinguish clearly. For example:

(1) The average car travels kilometers per minute. How many kilometers does it travel in 30 minutes? The quantitative relationship of this kind of problem is consistent with seeking the sum of an addend in an integer, or 30 times.

② 10 egg weight kg. How many kilograms does each egg weigh on average? The quantitative relationship of this problem is consistent with the integer division problem.

In addition to the quantitative relationship of integer multiplication and division, the application problem of fractional multiplication and division has new quantitative relationships, which are usually divided into three situations, or three basic application problems of fractions: (1) the application problem of finding a number that is a fraction of another number. (2) The multiplication problem of finding the fraction of a number. (3) Know the fraction of a number and find the division of this number. (There is no such name in the new syllabus. For the convenience of analysis, the author uses these common names. If the above three situations are percentages, then these three situations are the three basic application problems of percentages. I have to explain here that the new syllabus only asks for four application problems of the score, including the practical application of engineering problems and percentages, and does not specify which application problems to teach. Considering the different styles of textbooks, there may be some choices, so we should study the teaching requirements according to the contents of the current general textbooks for reference.