This part of the extended materials mainly examines the knowledge points of division:

The dividend is enlarged (reduced) by n times, and the quotient is correspondingly enlarged (reduced) by n times under the condition that the divisor is unchanged. The divisor is expanded (reduced) by n times, while the dividend is unchanged, and the quotient is correspondingly reduced (expanded) by n times.

Dividing by two divisors in succession is equal to dividing by the product of these two divisors. Sometimes simple operations can be performed according to the nature of the division. For example, 300÷25÷4=300÷(25×4) divided by a number is equal to the reciprocal of this number.

If the quotient of divisor must be an integer, and the divisor and dividend are not factors, there will be a difference, and the difference (D below) is the remainder.

Long division, commonly known as "long division", is suitable for formal division, fractional division, polynomial division (that is, factorization) and other divisions that pay more attention to the calculation process and quotient, and both multiplication and subtraction are used in the process. According to the multiplication table, two integers can be calculated by long division (direct division). If the dividend has a decimal part (or decimal point), just bring the decimal point down when calculating; If the divisor has a decimal point, move the decimal points of the divisor and the dividend at the same time until the divisor has no decimal point. An abacus can also do division.