A is called the first term of the ratio, and b is called the last term of the ratio. The quotient of a÷b is called the ratio of a ∶ b.

Among the meanings and properties of cognitive ratio, the significance of cognitive ratio is the key, and the basic properties of ratio are obtained in the practice of meaning association of ratio. The core of understanding the meaning of ratio lies in summarizing the definition of ratio.

Understand the meaning of ratio:

(1) Significance of analysis ratio

② Understanding of defining elements.

A÷b is called a∶b, which means that the ratio belongs to another form of "division" and mainly represents the relationship between two numbers.

The division of two similar quantities refers to the division of numbers with the same unit name and the division of two numbers without unit name. If the dividend and divisor are extended to divide by different quantities, just study the relationship between the two divisors, which can also be called ratio.

The same amount is divided. Find the number of copies in the relationship between the total number and the number of copies. Find multiples in the multiple relationship; Divide different kinds of quantities, find each part in the relationship between the total number and the number of copies, and double it in the relationship between multiples.

Students learn by consulting "small materials" provided by textbooks:

In A: B, A is called the former term of the ratio, and B is called the latter term of the ratio (the latter term of the ratio cannot be 0).

The quotient obtained by dividing the former term of the ratio by the latter term of the ratio is called the ratio.

According to the definition of ratio, carry out association exercises:

According to the understanding of the definition of contrast, the definition of ratio is extended to: division of two numbers, also known as the ratio of two numbers.

② The relationship among ratio, fraction and division.

The difference between ratio, division and fraction, ratio is considered by comparing the relationship between two numbers (quantities), except that it is an operation, and fraction represents a number.

③ According to the relationship between ratio and fraction (or division), the basic properties of ratio are obtained:

The size of this value will not change.

The first and second items of the ratio are multiplied or divided by the same number (except zero), and the ratio remains unchanged.

At the same time, several other properties of the ratio are derived from the division equation and the "change of quotient":

According to "dividend = divisor × quotient":

The former term of the ratio = the latter term of the ratio × the ratio.

According to "divisor = dividend quotient", the latter ratio = the former ratio is obtained.

According to "the dividend is expanded (or reduced) several times, the divisor remains unchanged, and the quotient is also expanded (or reduced) by the same times", it is concluded that "the former term of the ratio is expanded (or reduced) several times, and the latter term of the ratio remains unchanged, and the ratio is also expanded (or reduced) by the same times. That is, if a: b = q, then (a× m): b = q× m or (a ∶ m): b = q: m (m ≠ 0).

According to "the dividend is constant, the divisor is expanded (or reduced) several times, and the quotient is reduced (or expanded) by the same times." It is concluded that the former item remains unchanged, and the latter item is expanded (or reduced) several times, but the proportion is reduced (or expanded) by the same multiple. That is, if a: b = q, then a: (b× m) = q ≠ m (m ≠ 0) or a: (b ≠ m) = q× m (m ≠ 0).

According to dividend > divisor, quotient > 1. Dividend = divisor, quotient = 1. Divider b, then q > 1. On the other hand, if q < 1, then a < b；; If q= 1, then a = b；; If q > 1, then a > b.

(4) According to the definition of ratio, write the method of calculating ratio.