Answer:
11/14
4/5
9/11
Explanation:
To find rational numbers between 2/3 and 5/7, we can follow a methodical approach by creating fractions with common denominators and then selecting values in between. Here's how I got those answers:
11/14: I chose a denominator that is a common multiple of 3 and 7, which is 21. Then, I looked for a numerator that is between 2/3 and 5/7 when expressed with this denominator. 11/14 falls between these two fractions because:
2/3 is approximately equal to 14/21.
5/7 is also equal to 15/21.
So, 11/14 is between 14/21 and 15/21.
4/5: To find another fraction between 2/3 and 5/7, I used a common denominator approach. The common denominator for 3 and 7 is 21. Now, I compared the fractions:
2/3 is equal to 14/21.
5/7 is equal to 15/21.
Since 4/5 is less than 15/21 and greater than 14/21, it is between 2/3 and 5/7.
9/11: Again, I found a common denominator for 2/3 and 5/7, which is 21. Then, I checked where 9/11 fits in between:
2/3 is equal to 14/21.
5/7 is equal to 15/21.
9/11 is greater than 14/21 but less than 15/21, making it a rational number between 2/3 and 5/7.
These fractions were selected by finding common denominators and identifying values within the given range.