Short answer: you are correct.
Given
a) 2/3 and 3/5
b) 6/15 and 3/7
Find
the appropriate relation symbol (< or >)
Solution
There are several ways you can compare fractions like this. One way is to convert them to fractions with the same numerator or denominator. Another way is to convert them to decimal fractions. Yet another is to multiply them by some value that converts them both to integers (essentially equivalent to finding a common denominator).
a) 2/3 ≈ 0.67 and 3/5 = 0.60, so 2/3 > 3/5
Alternatively, multiply both by 15: (2/3)×15 = 10; (3/5)×15 = 9. 10 > 9.
You can multiply 2/3 by 3 to make the numerator 6: 2/3 = 6/9.
You can multiply 3/5 by 2 to make its numerator 6: 3/5 = 6/10. Then the fraction with the smaller denominator is the larger fraction: 6/9 > 6/10.
b) It is convenient to use the last of the above approaches to make 3/7 have a numerator of 6. Now, you're comparing 6/15 vs 6/14.
... 6/15 < 6/14, so 6/15 < 3/7
Once again, you can compare the decimal:
... 6/15 = 2/5 = 0.40 and 3/7 ≈ 0.43, so 6/15 < 3/7