<P> Two numbers can be multiplied as in this example: To multiply 5 × 3, note that this is the same as 5 + 5 + 5, so pick up the length from 0 to 5 and place it to the right of 5, and then pick up that length again and place it to the right of the previous result . This gives a result that is 3 combined lengths of 5 each; since the process ends at 15, we find that 5 × 3 = 15 . </P> <P> Division can be performed as in the following example: To divide 6 by 2--that is, to find out how many times 2 goes into 6--note that the length from 0 to 2 lies at the beginning of the length from 0 to 6; pick up the former length and put it down again to the right of its original position, with the end formerly at 0 now placed at 2, and then move the length to the right of its latest position again . This puts the right end of the length 2 at the right end of the length from 0 to 6 . Since three lengths of 2 filled the length 6, 2 goes into 6 three times (that is, 6 ÷ 2 = 3). </P> <Ul> <Li> <P> The ordering on the number line: Greater elements are in direction of the arrow . </P> </Li> <Li> <P> The difference 3 - 2 = 3 + (- 2) on the real number line . </P> </Li> <Li> <P> The addition 1 + 2 on the real number line </P> </Li> <Li> <P> The absolute difference . </P> </Li> <Li> <P> The multiplication 2 times 1.5 </P> </Li> <Li> <P> The division 3 ÷ 2 on the real number line </P> </Li> </Ul> <Li> <P> The ordering on the number line: Greater elements are in direction of the arrow . </P> </Li>

The length of a line segment is always negative