Question

Insert five rational numbers between the following rational numbers:

`1/2` and `5/14`

Answer 1

Given: Insert five rational numbers between `1/2` and `5/14`.

Stepwise Calculation:

1. First, express both fractions with a common denominator for easy comparison.

`1/2 = 7/14` and `5/14` remains the same.

Here, `5/14 < 1/2`, so the numbers between them should lie between `5/14` and `7/14`.

2. To find rational numbers between two fractions, find values between `5/14` and `7/14` with denominators larger than 14 or equivalently, find increments between the two fractions divided into smaller steps.

3. Alternatively, scale the fractions to have a larger denominator to insert more rational numbers easily, for example, multiplying numerator and denominator by 10:

`5/14 = 50/140`,

`7/14 = 70/140`

4. Now, rational numbers between `50/140` and `70/140` are those with numerators between 50 and 70 over 140. 

We can select:

`51/140, 52/140, 53/140, 54/140, 55/140`

These can be simplified if possible.

5. Specifically, according to the source, the five rational numbers inserted between `1/2` and `5/14` are `51/140, 13/35, 53/140, 27/70, 11/28`.

Five rational numbers between `1/2` and `5/14` are `51/140, 13/35, 53/140, 27/70, 11/28`.

These lie strictly between `5/14` and `1/2` as required.