Representation of 5/7 on the Number Line

To represent the rational number 5/7 on the number line, we need to follow the steps given below:

1. Draw a number line: Draw a straight line and mark a point O on it to denote the origin.

2. Mark the unit distance: Divide the line into equal parts and mark each part as a unit distance. Label each unit with a number starting from 0.

3. Locate the numerator: Since the numerator of 5/7 is 5, we need to locate the point 5 on the number line. For this, we need to count 5 units to the right of the origin and mark the point as A.

4. Divide the line into equal parts: Divide the unit distance into seven equal parts.

5. Locate the denominator: Since the denominator of 5/7 is 7, we need to locate the point 7 on the number line. For this, we need to count 7 units to the right of the origin and mark the point as B.

6. Join the points: Draw a line segment joining the points A and B. This line segment represents the rational number 5/7 on the number line.

Explanation

The rational number 5/7 lies between 0 and 1 on the number line. It is closer to 1 than to 0 since the numerator is greater than the denominator. The point A lies to the left of the point B, which indicates that the rational number is less than 1. The line segment AB represents all the possible values of the rational number 5/7. We can see that there are infinitely many other rational numbers on the number line, and the distance between any two adjacent numbers is equal. The representation of rational numbers on the number line helps us to compare them, find their order, and perform arithmetic operations.