Explanation

One ratio is 3\;:\;5 or \large\frac{3}{5} .
And the other ratio is 4\;:\;7 or \large\frac{4}{7} .
Now, LCM of 5 and 7 is = 35.
So,
3\;:\;5=\large\frac{3}{5}\normalsize=\large\frac{3\times7}{5\times7}\normalsize=\large\frac{21}{35} _{[convert equal denominator]}
4\;:\;7=\large\frac{4}{7}\normalsize=\large\frac{4\times5}{7\times5}\normalsize=\large\frac{20}{35} _{[convert equal denominator]}
Now, we see that \large\frac{21}{35} is greater then \large\frac{20}{35} .
Ans: 3\;:\;5 is greater than 4\;:\;7 .

Another form of this specific math question exists:

1. Comparing the ratios 3:5 and 4:7, which one is greater?
2. When comparing 3:5 and 4:7, which ratio denotes a larger quantity?