concept

Ratio refers to the relative size relationship between two quantities, which is usually used to express the proportional relationship between two quantities. In mathematics, the ratio is usually expressed by a colon or a diagonal line, such as a:b or A/B. The concept of ratio can be used to compare the difference between two quantities, calculate the average value, and solve other mathematical problems related to proportion.

Definition of mathematical ratio

Mathematically, the ratio of two numbers refers to the result of division of two numbers. That is to say, if we have two numbers A and B, their ratio a:b is the result of A divided by B. For example, if we have two numbers 3 and 4, their ratio is 3:4, which means 3 divided by 4.

The nature of mathematical ratio

Mathematical ratios have some important properties. For example, for any two nonzero numbers A and B, their ratio a:b is always equal to b:a, that is, the ratio of the two numbers is unique. In addition, if the ratio of two numbers is equal, then the two numbers are equal. These properties are very important in solving practical problems.

Knowledge points and differences of ratio and proportion

Knowledge of ratios and proportions

Ratio and proportion have always been one of the most puzzling problems in learning mathematics. In fact, the problem between the two can be completely summarized in one sentence: the ratio is equivalent to the formula on the left of the equal sign in the formula, which is one of the formulas (for example, a:b). The ratio is formed by connecting at least two formulas called the ratio with an equal sign, and the ratio of these two ratios is the same (for example, a:b=c:d).

The difference between ratio and proportion

1, meaning, item number and part name are different. A ratio is the division of two numbers, and there are only two terms: the first term and the last term of the ratio. For example: a:b This is a ratio and an equation, which means that two ratios are equal, and there are four terms: two external terms and two internal terms. A:b=3:4 This is the ratio.

2. The basic nature of ratio and the basic nature of proportion have different meanings and applications. The nature of the ratio: the first term and the last term of the ratio are multiplied or divided by a nonzero number. This ratio remains unchanged. The essence of proportion: in proportion, the product of two external terms is equal to the product of two internal terms. The nature of the ratio is used for the solution ratio. Connection: Proportion consists of two equal proportions.