Final answer:
To find three rational numbers between 3/7 and 2/3, multiply the denominators (7 and 3) to get a common denominator of 21, then find fractions with numerators between the equivalents of these two fractions (9/21 and 14/21). Suitable examples are 10/21, 11/21, and 12/21.
Step-by-step explanation:
To find three rational numbers between 3/7 and 2/3, first we can find a common denominator for the two fractions. We can do this by multiplying the denominators together. For 3/7 and 2/3, the denominators are 7 and 3, respectively, and when multiplied, we get a common denominator of 21. Now, let's express 3/7 and 2/3 with the common denominator 21.
For 3/7, we multiply both the numerator and denominator by 3 to get 9/21, and for 2/3, we multiply both the numerator and denominator by 7 to get 14/21. Thus, the two fractions are equivalent to 9/21 and 14/21 respectively. To find numbers between them, we can simply find fractions with the same denominator of 21 whose numerators are between 9 and 14.
Three such fractions can be 10/21, 11/21, and 12/21. These are all between 9/21 (3/7) and 14/21 (2/3), making them rational numbers situated between the two given fractions.