Question

by average method insert three rational number between -3and 5/6​

Answer 1

Answer:

We need to find three rational numbers between them. so both the numerator and denominator should be multiplied by 4 as the LCM is 4. (5+6)/2=5.5.

Answer 2

As you might guess, you can use the same methods in that reply to get your answer.

There is not ONE answer, so we cannot ask for “the rational number”

There are an infinite number of answers, so we cannot ask for “the rational numbers”

There are many methods of finding rational numbers:

Average your two two numbers, you will find a rational number

Calculate 34+56=912+1012=9+1012=???

Divide that sum by two to get the average.

That answer is a rational number between your two numbers.

Do a weighted average. Add seven times your first number plus three times your second number, then divide the sum by ten.

Calculate: 7×34+3×56=214+156=???

Divide that answer by 10 (because 7+3=10)

The answer will be between your two numbers.

With fractions like 34 and 56 , you can do DIRTY ADDITION:

Add the numerators: 3 + 5 = 8

Add the denominators: 4 + 6 = 10

Write your new fraction and simplify:

34+56→3+54+6=810=???

This “dirty” answer is between your two numbers

Another trick you can use with fractions: Convert BOTH fractions to a common denominator, not necessarily the lowest common denominator, then list all the fractions between those two fractions.

34<56

7296<8096

7396,7496,…

How many rational numbers could you find if you used 9600 as the common denominator?

There are other methods. See my other answer for other methods, including ways to let your calculator do some work for you

I hope you are understand my solution