Question

Insert two rational numbers between the following rational numbers:

`3/5` and `5/6`

Answer 1

Given: Insert two rational numbers between the rational numbers `3/5` and `5/6`.

Step-wise calculation:

1. Find a rational number between `3/5` and `5/6` using the formula for the average of two rational numbers: 

A rational number between `3/5` and `5/6 = (3/5 + 5/6)/2`

= `(18/30 + 25/30)/2`

= `43/30 xx 1/2`

= `43/60` 

Since `3/5 < 43/60 < 5/6, 43/60` is a rational number between the given two.

2. Now, find a rational number between `43/60` and `5/6`: 

A rational number between `43/60` and `5/6`

= `(43/60 + 5/6)/2`

= `(43/60 + 50/60)/2`

= `93/60 xx 1/2`

= `93/120`

Since `43/60 < 93/120 < 5/6, 93/120` is also a rational number between the given two.

Two rational numbers between `3/5` and `5/6` are `43/60` and `93/120`.