5. Comparison of rational numbers

Representation of rational numbers on number line
Draw a straight line. Take a point O on it. Call it 0 (zero). Set off equal distances on its right as well as on the left of 0. Such a distance is known as a units length. Clearly, the points A, B, C, D, E represent the integers 1, 2, 3, 4, 5 respectively and the points A', B', C', D', E' represent the integers –1, –2, –3, –4, –5 respectively.

Thus, we may represent any integer by a point on the number line. Clearly, every positive integer lies to the right of O and every negative integer lies to the left of O. 

Illustration 2    

Solution:    
        Draw a line, take a point O on it, let it represent 0.

From O, set off unit distances OA, AB and BC to the right of O. Clearly, the points A, B and C represent the integers 1, 2 and 3 respectively. Now, take 2 units OA and AB, and divide the third unit BC into 5 equal parts. Take 3 parts out of these 5 parts to reach at a point P. Then the point P represents the rational number 

Again, from O, set off unit distances to the left. Let these segments be OA’, A’ B’, B’C’, etc. Then, clearly the points A’, B’ and C’ represent the integers –1,–2,–3 respectively.

Take 2 full unit lengths to the left of O. Divide the third unit B’C’ into 5 equal parts. Take 3 parts out of these 5 parts to reach a point P’.

Then, the point P’ represents the rational number   

Thus, we can represent every rational number by a point on the number line.