The basic knowledge of leaving Hong Kong includes:

The meaning of division: knowing the product of two factors and one of them, the operation of finding the other factor is called division. Division is the inverse of multiplication.

Master trial-and-error method and calculate division vertically.

Division is divided into average division and inclusive division.

Invariant property of division quotient: the divisor and divisor are multiplied or divided by the same number (except 0) at the same time, and the quotient remains unchanged.

The continued division property: a number divided by several numbers equals a number divided by the product of these numbers.

Understand the relationship between fraction and division: numerator is equivalent to dividend, fractional line is equivalent to divisor and denominator is equivalent to divisor.

Understand the relationship between ratio and division: the former term of ratio is equivalent to dividend, and the latter term is equivalent to divisor.

2. Want to collect knowledge related to division

The symbol of division belongs to the symbol of four operations. The addition and subtraction signs in the four arithmetic operations began to be used in15th century, and the multiplication and division signs appeared in17th century.

The division symbol "∫" is called the Rennes symbol, because it first appeared in an algebra book published by Swedish Johann Liuinrich Rahn in 1622- 1676. 1668, this book was translated into English and published, and this symbol is popular today. He separated the two points with a horizontal line to show the meaning of decomposition, that is, "?" , respectively, representing the numerator denominator.

However, Leibniz, a famous German scientist, advocated replacing the symbol with ":". 1666, Leibniz first used ":"as a division symbol in his paper "The Art of Combination", which was used by both Germany and the former Soviet Union.

3. The fifth grade decimal multiplication and division knowledge summary,

1, Multiply (1) Integer by Decimal and Decimal by Decimal: Calculate the product by integer multiplication rule first, and then see how many decimal places there are in the factor. Calculates the product from right to left and points to the decimal point.

Note: If there is a zero at the end of the product, please point the decimal point first and then cancel it. 2. Division: (1) Fractional division in which the divisor is an integer: first calculate the quotient with the integer division law, and then put the decimal point on the quotient (the decimal point of the quotient should be aligned with the decimal point of the dividend).

(2) Divider is decimal: first move the decimal point of the divisor to make the divisor an integer, move the decimal point of the divisor a few places to the right, and move the decimal point of the divisor a few places to the right (if there are not enough digits, make up the divisor with 0), and then calculate according to the decimal divisor of the divisor as an integer.

4. How to organize and summarize the knowledge related to integer division in the whole primary school to form a knowledge network?

This study stems from the needs of practice. Although domestic scholars are concerned about integer division, there has never been a monograph on integer division in primary schools. This study lasted for half a year. In addition to the teaching of integer division in primary schools, interviews and literature were the main research methods.

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Huazhong normal university, 20 14

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Primary school mathematics/integer division/teaching problems/teaching strategies

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5. What is the basis of learning division?

Er, division is the problem of average score, and division is one of the four operations. Knowing the product of two factors and one of them, the operation of finding the other factor is called division. If ab=c(b≠0), the operation of finding another factor A by multiplying C and B is division.

Division, written as c/b, pronounced as c divided by b (or b divided by c). Among them, c is called dividend, b is called divisor, and the result of a operation is called quotient. For example, 10/5, the dividend is 10, the divisor is 5 and the quotient is 2. In non-algebraic writing, a/b can also be simply written as a ÷b B B. In most non-English languages, c/b can also be written as C: B. Please refer to the proportion for the usage of colon in English. Law of division: How many digits is the divisor? Look at the first few digits of the divisor first. If the first few digits are not divided enough, look at one more digit. Except for the one to which it belongs, all the vendors will write on it. It is not enough for quotient one and quotient zero to occupy one position. The remainder is less than the divisor. If the quotient is decimal, the decimal point of the quotient should be aligned with that of the dividend. If the divisor is a decimal, it must be divided into integers and then calculated. Quotient invariance: when the dividend and divisor are multiplied or divided by a non-zero natural number at the same time, the quotient remains unchanged.