Problem
Rewrite 2 m 55 cm, 2 m 89 cm, and 1 m 50 cm as 255 cm, 289 cm, 150 cm.
Since 1 m equals 100 cm, a length written in m and cm can be rewritten as one cm value, and same-unit lengths are what add and subtract cleanly.
Draw A Diagram2.MD.B.5Measuring LengthAdding A-C and B-D gives 544 cm, but the overlap is counted twice.
Span A-C is A-B plus B-C, and span B-D is B-C plus C-D, so adding the two spans lays the middle B-C down twice while every other part is laid down once.
Identify Subproblems2.MD.A.4Measuring LengthSubtract the overlapping 150 cm from 544 cm to get 394 cm = 3 m 94 cm.
The summed 544 cm counts the whole A-to-D path once but counts the middle overlap B-C a second time, so it is exactly one overlap too big. Subtracting that 150 cm once undoes the extra count and leaves A to D measured just once.
Identify Subproblems2.MD.B.5Measuring LengthTaking one copy of the overlap B-C (150 cm) out of the summed total (544 cm) leaves the exact length from A to D.
The summed total counts the whole path from A to D once but counts the middle overlap B-C a second time, so it is exactly one overlap too big.
The path from A to D is three touching parts in a row — A-B, then B-C, then C-D — with no gaps and no overlaps, so those parts add up to the whole path.
Span A-C is the parts A-B and B-C joined, and span B-D is the parts B-C and C-D joined, so adding the two spans lays the middle part B-C down twice while every other part is laid down once.
Subtracting one overlap takes back exactly the amount the second span piled on top, undoing the extra count and leaving A to D measured just once.
When two lengths overlap, add them and then subtract the overlap once to get the true total length.