INSERTING RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS

Example 1 :

List five rational numbers between –2 and 0.

Solution :

-1.9, -1.8, -1.7, -1.6, -1.5

writing the above decimals as rational numbers, we get

-19/10, -18/10, -17/10, -16/10, -15/10

Example 2 : 

List five rational numbers between -1/2 and 3/5.

Solution :

Let us convert the denominators same.

(-1/2) ⋅ (5/5)  =  -5/10

(3/5) ⋅ (2/2)  =  6/10

Rational numbers between them are 

-4/10, -3/10, -2/10, -1/10, 0, 1/10, .....

We may choose any five as answer.

Example 3 :

List five rational numbers between 0.25 and 0.35.

Solution :

Writing numbers between 0.25 and 0.35 in decimal form, we get

0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34

By changing them into fraction, we get

26/100, 27/100, 28/100, 29/100, 30/100

Example 4 :

List five rational numbers between –1.2 and -2.3.

Solution :

-1.3, -1.4, -1.5, -1.6, -1.7, .........., -2.2

By changing them into decimal form, we get

13/10, 14/10, 15/10, 16/10, 17/10.

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