Introduction: Rational numbers are those numbers which can be represented in the form p/q where p and q are integers and q is not equal to zero. In this question, we need to represent the given rational numbers on the number line.

Representation of Rational Numbers on a Number Line:

To represent rational numbers on a number line, we need to follow the below steps:

1. Draw a number line and mark the zero on it.

2. Divide the number line into equal parts.

3. Label the parts with integers.

4. Represent the given rational number on the number line by finding its approximate location between two integers.

Representation of Given Rational Numbers:

(i) -4/5:

-4/5 can be represented on the number line as follows:

-1 ---|---|---|---|---0---|---|---|---|---1

Here, -4/5 is approximately between -1 and -0.8, so we can represent it on the number line between -1 and -0.8.

(ii) 3/8:

3/8 can be represented on the number line as follows:

-1 ---|---|---|---|---0---|---|---|---|---1

Here, 3/8 is approximately between 0.2 and 0.5, so we can represent it on the number line between 0.2 and 0.5.

(iii) 5/4:

5/4 can be represented on the number line as follows:

-2 ---|---|---|---|---|---|---|---|---|---|---1

Here, 5/4 is approximately between 1.2 and 1.5, so we can represent it on the number line between 1.2 and 1.5.

(iv) -31/6:

-31/6 can be represented on the number line as follows:

-6 ---|---|---|---|---|---|---|---|---|---|---1

Here, -31/6 is approximately between -6 and -5.2, so we can represent it on the number line between -6 and -5.2.

(v) 8/7:

8/7 can be represented on the number line as follows:

-1 ---|---|---|---|---|---|---|---1

Here, 8/7 is approximately between 1.1 and 1.3, so we can represent it on the number line between 1.1 and 1.3.

Conclusion:

Thus, we can represent the given rational numbers on the number line by finding their approximate locations between two integers.

Represent the following rational number on the number line 2 1/5