Question

Insert one rational number between the following rational numbers:

`-2/5` and `-3/2`

Answer 1

Given: Insert one rational number between `-2/5` and `-3/2`.

Step-wise calculation:

1. Convert the two numbers into a comparable form:

`-2/5 = -0.4`,

`-3/2 = -1.5`

2. Since `-3/2 < -2/5`, the rational number between them must lie between –1.5 and –0.4.

3. One way to find a rational number between two given rational numbers a and b is to take their average: 

Average = `(a + b)/2`

4. Calculate the average:

`(-2/5 + (-3/2))/2 = (-2/5 - 3/2)/2`

5. Find common denominator and sum inside the numerator:

`-2/5 = -4/10`

`-3/2 = -15/10`

`-4/10 - 15/10 = -19/10`

6. Divide by 2:

`(-19/10)/2`

= `-19/10 xx 1/2`

= `-19/20`

A rational number between `-2/5` and `-3/2` is `-19/20`.

Thus, `-3/2 < -19/20 < -2/5`.