2/3and 6/11
22and18/33
22/33×10and 18/33×10
220/330 and180/330
the 6 rational number between to 220/330and 180/330 are 181/330,182/330,183/330,184/330,185/330,186/330

Introduction:

To find six rational numbers between 2/3 and 6/11, we need to understand what rational numbers are and how they can be represented. Rational numbers are numbers that can be expressed as a quotient or fraction of two integers, where the denominator is not zero. They can be positive, negative, or zero.

Method:

To find rational numbers between any two given rational numbers, we can follow the following steps:

Step 1: Convert the given rational numbers into decimals.
Step 2: Find the difference between the two decimals.
Step 3: Divide the difference by the number of rational numbers required plus one.
Step 4: Add the quotient obtained in step 3 to the decimal representation of the first rational number. Repeat this process to find the other rational numbers.

Example:

Given rational numbers: 2/3 and 6/11

Step 1: Convert the given rational numbers into decimals.
2/3 ≈ 0.6667
6/11 ≈ 0.5455

Step 2: Find the difference between the two decimals.
0.6667 - 0.5455 = 0.1212

Step 3: Divide the difference by the number of rational numbers required plus one.
0.1212 ÷ 7 = 0.0173

Step 4: Add the quotient obtained in step 3 to the decimal representation of the first rational number.
0.6667 + 0.0173 = 0.684

Repeat the process:
0.684 + 0.0173 = 0.7013
0.7013 + 0.0173 = 0.7186
0.7186 + 0.0173 = 0.7359
0.7359 + 0.0173 = 0.7532
0.7532 + 0.0173 = 0.7705

Therefore, six rational numbers between 2/3 and 6/11 are:
0.684, 0.7013, 0.7186, 0.7359, 0.7532, 0.7705

Conclusion:

By following the steps mentioned above, we can find six rational numbers between 2/3 and 6/11. These rational numbers are 0.684, 0.7013, 0.7186, 0.7359, 0.7532, and 0.7705.