1, the first term and the last term of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged. This property is called the basic property of ratio. This property is widely used in practical applications. For example, when solving the problem of fractions, we can change fractions into fractions with the same denominator, and then use the properties of ratios to simplify and compare sizes.
2. Before and after the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged. This property can also be called the stability of ratio. It shows that when the units of two quantities are different, the proportional relationship between them will not be affected. For example, speed is the distance divided by time, and its value is the same whether it is expressed in kilometers per hour or meters per second.
3. Ratio refers to the proportional relationship between two quantities. This ratio can be expressed in fractions, decimals or integers. In mathematics, the concept of ratio is very important and the key to solve many mathematical problems. For example, when solving the score problem, it is necessary to compare the sizes of two scores; When solving the proportion problem, it is necessary to calculate the proportion of two quantities and so on.
The purpose of the sixth grade math ratio:
1. Simplify the expression and solve the problem: the ratio can be used to simplify the mathematical expression and make the complex relationship more concise and clear. For example, when solving the problem of comparing fractions or percentages, we can compare their sizes more intuitively by converting different fractions or percentages into the same units and then comparing them. When solving the problem of proportional distribution, the ratio can also help us find the key to solve the problem quickly.
2. Data analysis: Ratio is one of the important tools for data analysis. By converting data into proportions or ratios, we can better understand the distribution and relationship of data. For example, in statistics, we often use proportions or ratios to describe and compare the distribution characteristics of different data. In addition, in finance, we will also use ratio to describe the index and yield of the stock market, so as to better understand the overall performance of the market.
3. Establish a mathematical model: the ratio can be used to establish a mathematical model. For example, when solving geometry problems, we often use proportions or similar concepts to compare the areas or perimeters of different figures. When solving algebraic problems, the ratio can also be used to describe the relationship between different equations or inequalities. By establishing a mathematical model, we can better understand the nature of the problem and find a solution to the problem.