In 1. division, the dividend and divisor are expanded or reduced by the same multiple at the same time, and the size of the quotient remains the same.

2. In division with remainder, the dividend and divisor are expanded or reduced by the same multiple at the same time, and the quotient is unchanged, and the remainder is expanded or reduced by the same multiple at the same time.

The definition of quotient:

Quotient is a mathematical term, and the formula is: (dividend-remainder) ÷ divisor = quotient, which is recorded as dividend ÷ divisor = quotient ÷ remainder. In a division formula, the relationship between dividend, remainder, divisor and quotient is: (dividend-remainder) ÷ divisor = quotient, which is recorded as dividend ÷ divisor = quotient ÷ remainder, and then the quotient × divisor+remainder = dividend is derived.

When the number A is divided by the number B (non-zero), its quotient is called complete quotient. For example, 9÷3=3, and 3 is the complete quotient. If the number A is divided by the number B (not 0), the quotient is incomplete. For example: 10 ÷ 3 = 3... 1, where 3 is an incomplete quotient.

Extended data:

Introduction to primary school mathematics;

Primary school mathematics is to teach children a series of knowledge about number, four operations, the calculation formula of figure and length, unit conversion and so on through textbooks, which lays a good mathematical foundation for junior high school and daily life calculation.

Frieden Noel, a Dutch educator, said: "Mathematics comes from reality and must be rooted in reality and applied to reality." Indeed, modern mathematics requires us to observe the world from a mathematical perspective and explain the world in mathematical language.

Judging from the mathematics learning psychology of primary school students, the learning process of students is not a passive absorption process, but a reconstruction process based on existing knowledge and experience. Therefore, learning while doing and learning while playing will make children learn more actively. From our educational goal, while imparting knowledge, we should pay more attention to cultivating students' comprehensive ability of observation, analysis and application.