含绝对值的问题,其解法大多有一定的技巧性,但只要我们充分理解绝对值的定义, 再根据题目的特点,选择适当的方法,那么问题就不难解决．本文结合2000年以来各省、市的竞赛题, 谈谈此类问题的题型和解法,以供参考．一、绝对值与数轴例1 (2000年第11届“希望杯”数学邀请赛初一试题)有理数a、b、c在数轴上的位置如图所示,若m=|a+b|-|b-1|-|a-c| -|1-c|,则1000m=____． With absolute values, most of their solutions have certain skill, but as long as we fully understand the definition of absolute values, and then select the appropriate method according to the characteristics of the topic, then the problem is not difficult to solve. This article combines the competition questions of provinces and cities since 2000, and talks about the types and solutions of such issues for reference. 1. Absolute value and number axis example 1 (The first question of the 11th “Hope Cup” mathematical tournament in 2000) The positions of rational numbers a, b and c on the number axis are shown in the figure, if m=|a+b|-| B-1|-|ac| -|1-c|, then 1000m=____.