1. Definition of division: Division is a basic mathematical operation, which refers to dividing a number (dividend) into several equal parts (divisor), and each part has the same size (quotient). For example, if there are 10 apples, and each person has two apples, then it can be distributed to five people. Where 2 is the divisor, 10 is the dividend, and 5 is the quotient.

2. Symbol of division: Division can be represented by \ u.. For example, 10÷2=5, which means that 10 divided by 2 equals 5.

3. The nature of division: division has reflexivity, interchangeability and combination. Reflexivity means that any number is divisible by itself equal to 1, commutativity means that two numbers are divisible by the same quotient, and associative law means that when three numbers are divisible, two numbers are divisible first and then the third number.

4. Relationship between division and multiplication: Division and multiplication are reciprocal operations. If a÷b=c, it can also be expressed as a = b × c, for example, 10÷2=5 can also be expressed as 10=2×5.

5. Calculation method of division: There are many calculation methods of division, including divisibility, division with remainder, cyclic division, etc. Divisibility refers to the case that both dividend and divisor are integers, and quotient is also integers.

Division with remainder refers to the case that both dividend and divisor are integers, but quotient is not integer. Cyclic division refers to the case that the dividend and divisor are decimals and the quotient is not an integer. Different calculation methods need to be selected according to the specific situation.

Application of division:

1. Divide items: In daily life, it is often necessary to divide items into several parts, each with the same size. For example, divide the cake into 8 pieces, each piece is equal in size, and everyone can get 1/8 pieces of cake. This sub-item problem can be solved by division.

2. Calculate percentage: percentage is a common division application. It is usually used to indicate the percentage of one number to another. For example, the sales of a company is 6,543,800,000 yuan, of which 200,000 yuan is profit, so the percentage of profit in sales is 20%. This problem of calculating percentage can be solved by division.

3. Find the unit cost: In the process of production or manufacturing, you need to calculate the unit cost, that is, the cost of each product. For example, if a company's total cost is 6.5438+0 million yuan and its total output is 6.5438+0 million products, the cost of each product is 6.5438+0 million yuan.

4. Calculation of speed and time: In traffic and sports, speed and time can be calculated by division. For example, a car travels 100 km and takes 2 hours, with an average speed of 50 km per hour. This problem of speed and time calculation can be solved by division.

5. Scientific experiment: In scientific experiment, division can be used to calculate the experimental results. For example, in chemical experiments, we can divide the mass of substances that react chemically to obtain parameters such as the rate and concentration of chemical reactions.