Ratio and proportion are important concepts in mathematics, and they are also one of the difficult parts to understand in the mathematics textbooks of Shanghai Education Press. The concepts of ratio and proportion are widely used in mathematics and real life, so it is very important for students to master the knowledge of ratio and proportion.

Ratio refers to the relative size relationship between two quantities of the same kind, usually expressed by two numbers separated by colons, such as 3: 4. The ratio can be used to compare the quantity, size, weight and so on between different items. The calculation of ratio includes finding ratio and simplifying ratio. To find a ratio is to divide one number by another, and to simplify the ratio is to divide two numbers in the ratio by their greatest common divisor at the same time to get the simplest ratio.

Proportion refers to two equal formulas, such as 3: 4 = 6: 8. Proportion can be used to solve many practical problems, such as calculating the price of goods and determining the proportion of materials. The calculation of the ratio includes judging whether the two ratios are proportional, finding the unknown in the ratio and so on.

In the mathematics textbook of Shanghai Education Edition, comparison and proportion are difficult, mainly because these two concepts are abstract and require students to have certain mathematical thinking ability and imagination. In addition, ratio and proportion are widely used, which requires students to master certain practical problems and solutions.

Problem solving skills of ratio and proportional application problems;

1, understand the meaning of the question and clarify the proportional relationship.

When solving the application problem of ratio and proportion, the first thing to do is to carefully examine the problem, understand the situation described by the problem, and make clear the proportion relationship involved. For example, when it comes to the ratio between two quantities, it is necessary to clarify which quantity is large and which quantity is small, and what is the ratio between them.

2. Solve the equation by using the proportional property.

Proportion has many important properties, such as combined ratio, divided ratio and equal ratio. When solving problems, we can make use of these properties, list the equations according to the proportional relationship given by the topic, and then solve them. This method is especially suitable for complex proportional problems and can simplify the calculation process.

3, draw a chart or modeling, intuitive problem solving.

For some ratio and proportion problems, drawing or modeling can reveal the essence of the problem more intuitively. For example, when solving problems involving multiple quantities or multiple proportions, we can draw a scale diagram or establish a mathematical model to find out the answer through observation and calculation. This method can not only improve the efficiency of problem solving, but also help to understand the deep meaning of the problem.