Number line
The integers can be represented on the number line. The positive integers lie to the right side and the negative integers to the left side of the zero point O.
Represent and on the number line.
(i) Draw a line and mark the zero point O on it.
(ii) Mark unit lengths OA and OA' to the right and left of O respectively. Then A represents the integer 1 and A' represent the integer -1.
(iii) Trisect OA and OA' as shown. Then OP represents and OP' represents .
Represent (i) and , (ii) and on the number line.
Repeat steps (i) and (ii) of earlier Example to get points A and A'; Divide OA and OA' into 4 equal parts each. Mark the points P, Q, P', Q' as shown.
Then P represents , P' represents
Q represents , Q' represents
Represent on the number line. This can be done in two ways.
1. We know that
Make a number line and mark points A, B,C, A',Bâ€™ and Câ€™ to represent 1, 2, 3, âˆ’ 1, âˆ’ 2 and âˆ’ 3 respectively.
Divide BC into 2 equal parts. Mark the middle point as P.
Then P represents 2 + = .
In the same way, divide B'C' into 2 equal parts. Mark the middle point as P'
Then P' represents.
Aliter
Make a number line and locate the point A representing the positive integer 5 on it.
Divide OA into 2 equal parts. Take one of these parts and mark point P. Then P represents
the rational number .
In the same way P' represents .