1, the meaning of fractional division:

Multiplication: factor × factor = product division: product ÷ one factor = another factor.

Fractional division has the same meaning as integer division, which refers to the operation of knowing the product of two factors and one of them and finding the other factor.

2, the calculation rules of fractional division:

Dividing by a number that is not zero is equal to multiplying the reciprocal of this number.

Law (when fractional division is relatively large):

(1) When the divisor is greater than 1, the quotient is less than the dividend;

(2) When the divisor is less than 1 (not equal to 0), the quotient is greater than the dividend;

(3) When the divisor is equal to 1, the quotient is equal to the dividend.

"[]" is called a bracket. In an equation, if there are both parentheses, you should count the parentheses first and then the parentheses.

Second, fractional division to solve the problem

(Unknown unit "1") (divided by division): What fraction of the known unit "1"? Find the number of units "1". )

1, the relationship between quantity and fractional multiplication is the same:

(1) is the "de" before the score: the quantity of the unit "1" × the score = the quantity corresponding to the score.

(2) Before the score, it means "more or less": the quantity of unit "1" ×( 1 fraction) = the quantity corresponding to the score.

2. Solution: (Suggestion: It is best to solve by equation)

Equation (1): Let the unknown quantity be x according to the quantitative relation and solve it by equation.

(2) Arithmetic (division): the quantity corresponding to the score ÷ the quantity corresponding to the score = unit "1".

3. Find the fraction of one number to another: just one number ÷ another number.

4. Find out how much one number is more (less) than another: the difference between two numbers ÷ unit "1" or:

① Find one more fraction: large number ÷ decimal number–1.

② Decimal: 1- decimal ÷ large number

Third, the ratio and the application of the ratio

(A), the meaning of the ratio

1, the meaning of ratio: the division of two numbers is also called the ratio of two numbers.

2. In the ratio of two numbers, the number before the comparison sign is called the first item of the ratio, and the number after the comparison sign is called the last item of the ratio. The quotient obtained by dividing the former term by the latter term is called the ratio.

For example,15:10 =15 ÷10 = 3/2 (the ratio is usually expressed as a fraction and can also be expressed as a decimal or an integer).

∶ ∶ ∶ ∶

The ratio of the former to the latter.

3. The ratio can represent the relationship between two identical quantities, that is, the multiple relationship. You can also use the ratio of two different quantities to represent a new quantity. For example: distance-speed = time.

4. Discrimination rate and ratio

Ratio: indicates the relationship between two numbers, which can be written in the form of ratio or fraction.

Ratio: equivalent to quotient, it is a number, which can be an integer, a fraction or a decimal.

According to the relationship between fraction and division, the ratio of two numbers can also be written as a fraction.

7. Difference between ratio, division and fraction: Division is an operation, and fraction is a number, and ratio represents the relationship between two numbers.

8. According to the relationship between ratio and division and fraction, it can be understood that the latter term of ratio cannot be 0.

In the sports competition, the scores of the two teams are 2: 0, etc. This is just a form of scoring, which does not represent the division of two numbers.

(B) The basic nature of the ratio

1, according to the relation of ratio, division and fraction:

The property that the quotient is invariant: the dividend and divisor are multiplied or divided by the same number at the same time (except 0), and the quotient is invariant.

The basic property of a fraction: when the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), the value of the fraction remains unchanged.

The basic nature of the ratio: the first and last items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

2. The simplest integer ratio: the first and last terms of the ratio are integers and prime numbers, so this ratio is the simplest integer ratio.

3. According to the basic properties of the ratio, the ratio can be reduced to the simplest integer ratio.

4. Simplified ratio:

(2) Using the method of calculating the ratio. Note: The final result should be written in the form of ratio.

For example:15:10 =15 ÷10 = 3/2 = 3: 2.

5. Proportional allocation: allocate a quantity according to a certain proportion. This method is usually called proportional distribution.

If the ratio of two quantities is known, let these two quantities be.

The distance is fixed, and the speed ratio is inversely proportional to the time ratio. (For example, for the same distance, the speed ratio is 4: 5 and the time ratio is 5: 4).

The total amount of work is certain, and the work efficiency is inversely proportional to the working hours.

(For example, the total amount of work is the same, the working time ratio is 3: 2, and the working efficiency ratio is 2: 3)