First, understand the definition of the absolute value of the number A. In middle school mathematics textbooks, the absolute value of the number A is defined as follows: "On the number axis, the distance from the point representing the number A to the origin is called the absolute value of the number A." Learning this definition should make students understand that the absolute value of the number A represents the distance between two points, and it should represent a non-negative number.

Second, to find out how to find the absolute value of the number A, we can know from the definition of the absolute value of the number A that the absolute value of a positive number is itself, the absolute value of a negative number is its reciprocal, and the absolute value of zero is zero. Here, students should focus on understanding how to express the reciprocal of a when a is negative, and the dual function of absolute value sign.

Third, master several common questions in junior high school mathematics to remove absolute value symbols.

1. For a class of problems in the form ︱a︱.

As long as we judge the three conditions of a according to the three properties of absolute value, we can quickly remove the absolute value symbol.

When a>0, ︱a︱=a (attribute 1, the absolute value of positive number is itself);

When a=0-A = 0 (property 2, the absolute value of 0 is 0);

When a< is at 0 o'clock; A =–a (property 3, the absolute value of a negative number is its reciprocal).

2. For a class of problems in the form ︱a+b︱.

As long as a+b is regarded as a whole, we can judge three situations of a+b, and according to the three properties of absolute value, we can quickly remove the absolute value symbol and simplify it correctly.

When a+b > 0, ︱a+b︱=a +b (property 1, the absolute value of a positive number is itself);

When a+b=0, ︱a+b︱=0 (property 2, the absolute value of 0 is 0);

When a+b

3. For a class of problems in the form ︱a-b︱.

Similarly, according to the above method, we still regard a-b as a whole, judge the three situations of a-b, and remove the sign of absolute value according to the three properties of absolute value.

However, errors are most likely to occur when deleting parentheses. How to get rid of the absolute sign quickly, the condition is simple, as long as you can judge the size of A and B. Because ︱ big-small ︱ = small-big-small, when a>b, ︱ A-B ︱ = A-B, ︱.

4. For a class of number axis problems,

Simplifying according to the formula of 3 is faster and more effective. For such a problem as ︱a-b︱, as long as A is judged to be on the right side of B, you can get ︱ A-B ︱ = A-B, ︱ B-A ︱ = A-B.

5. For operations with three or more absolute numbers.

Never change from its ancestors, or compare the formula in the absolute number as a whole with 0. If it is greater than 0, directly remove the absolute number and add a negative sign in front of the integer less than 0.