First, let's understand the question. We are asked to find out which of the given numbers is a common denominator of the two fractions, 3/4 and 1/5.
A common denominator of two fractions is a number, which is a multiple of the denominators of these fractions.
Step 1: Making equivalent fractions.
To make an equivalent fraction of 3/4, we multiply both the numerator (the top number) and denominator (the bottom number) by the same number. We can make equivalent fractions by multiplying by 5, 7, 10, which give us fractions (15/20, 21/28, 30/40) respectively.
Similarly, we can generate equivalent fractions for 1/5 by multiplying the numerator and denominator by 3, 7, 4 to give us the fractions (3/15, 7/35, 4/20) respectively.
Step 2: Comparing the denominators of these equivalent fractions with the given denominators.
Comparing the denominators of these equivalent fractions to the numbers given in the question (35, 15, 20, 30), we see that there is no denominator that is common between the two sets of fractions.
Therefore, we conclude that there is no common denominator for the fractions 3/4 and 1/5 among the numbers given in the question (35, 15, 20, 30).