Mr. marquis had a metal pipe that was 1,000 cm in length. he cut the pipe into 16 shorter pieces of equal length. how long was each piece?

To answer this, divide 1000 cm by 16:

1000 cm

= 66 2/3 cm per piece

  16 pieces

1) Given
2) Adding segments AB and BC together gives AC (Addition postulate, not too sure about the terminology) 
3) Segment Addition postulate 
4) Segment Addition postulate(Knowing that AC=BD, the distance between BC and CD add up to BD, shown in #3. AB and BC add together to give AC) 
5) Subtraction property of Equality 

Hope I helped :)