Question

insert three rational numbers between 1/2 and 3/5​

Answer 1

Answer:

The rational numbers in (1), (2) and (3) are three rational numbers between the original pair  ab  and  cd .

Step-by-step explanation:

There are many rational numbers between  12  and  35 .

You can find one of them by taking the average of those two rational numbers. That is, add them together and then divide by  2  (or multiply by  12 ).

If you want another rational number you can do the same by taking the previous answer and averaging it with either of the other rational numbers. If you want a third do it one more time.

In general here is a way to find those three rational numbers between two distinct rational numbers  ab<cd .

First, find the average between those two rational numbers as

(ab+cd)121

Second, take the average of (1) with  ab .

((ab+cd)12+ab)122

Finally, take the average of (1) with  cd :

((ab+cd)12+cd)123

The rational numbers in (1), (2) and (3) are three rational numbers between the original pair  ab  and  cd .