The knowledge points that must be tested in the first volume of sixth grade mathematics are as follows:

1, fractional multiplication: the numerator of a fraction is multiplied by the numerator and the denominator is multiplied by the denominator, so that the fraction can be reduced first.

2. Calculation rules of fractional multiplication: Fraction is multiplied by integer, numerator is the product of numerator multiplied by integer, denominator is unchanged, numerator is the product of numerator multiplied by fraction, denominator is denominator, but numerator denominator cannot be zero.

3. Significance of fractional multiplication: The significance of fractional multiplication of integers is the same as that of integer multiplication, and finding the sum of several identical addends is a simple operation.

4. Fraction multiplied by integer: combination of numbers and shapes, and conversion.

5. The basic nature of the ratio: the first and last items of the ratio are multiplied or divided by a non-zero number.

Many mathematical objects, such as numbers, functions and geometry, reflect the internal structure of continuous operations or the relationships defined in them. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations.

In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.

Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra.