The points of rational numbers a, B and C on the number axis correspond to a, B and C respectively, and their positions are shown in the figure, simplifying | C | - | C + B | + | a-c | + | B + a |

The points of rational numbers a, B and C on the number axis correspond to a, B and C respectively, and their positions are shown in the figure, simplifying | C | - | C + B | + | a-c | + | B + a |

∵ from the positions of a, B and C on the number axis, we can see that B < C < 0 < A, C + B < 0, a-c > 0, a + B < 0, the original formula = - C + C + B + a-c-a-b = - C

The corresponding points of rational numbers a, B and C on the number axis are a, B and C, and their positions are shown in the figure. Try to simplify them: | a + B | + | C-A | - | B + C |
B-----C-----0-----A-----→

From the graph, a > 0, C < 0, B < 0, | b > | C |, | B | > | a |, so a + B < 0, | a + B | = - A-B, C-A < 0, so | C-A | = a-c, B + C < 0, so | B + C | = - (B + C). So, the original formula = - A-B + a-c + B-C = - 2C

The position of rational number a and B on the number axis is shown in the figure
a 0 b
Simplification: |a + B | + |a-b | - |a | + |b|

a0 a+b