Question

Insert 9 rational numbers between the following rational numbers:

`3/2` and 2

Answer 1

Given: Two rational numbers `3/2` and 2, we need to insert 9 rational numbers between them.

Step-wise calculation:

1. Let `a = 3/2` and b = 2 and let the number of rational numbers to be inserted between a and b be n = 9.

2. Calculate the difference between b and a: 

`b - a = 2 - 3/2`

= `4/2 - 3/2`

= `1/2`

3. Divide this difference into n + 1 = 10 parts:

`(b - a)/(n + 1)`

= `(1//2)/10`

= `1/20`

4. The rational numbers inserted will be:

`a + (1(b - a))/10, a + (2(b - a))/10, ..., a + (9(b - a))/10`

5. Calculate each:

`3/2 + 1/20 = 30/20 + 1/20 = 31/20`

`3/2 + 2/20 = 30/20 + 2/20 = 32/20 = 8/5`

`3/2 + 3/20 = 33/20`

`3/2 + 4/20 = 34/20 = 17/10`

`3/2 + 5/20 = 35/20 = 7/4`

`3/2 + 6/20 = 36/20 = 9/5`

`3/2 + 7/20 = 37/20`

`3/2 + 8/20 = 38/20 = 19/10`

`3/2 + 9/20 = 39/20`

The 9 rational numbers between `3/2` and 2 are `31/20, 8/5, 33/20, 17/10, 7/4, 9/5, 37/20, 19/10, 39/20`.