To find the ratio of females to males in the gardening club, we start by determining the number of females.
There are a total of 60 members, with 9 being males. Therefore, the number of females is:
\[ 60 - 9 = 51 \]
Now, we can express the ratio of females to males:
\[ \text{Ratio of females to males} = \frac{\text{Number of females}}{\text{Number of males}} = \frac{51}{9} \]
To simplify this ratio, we can divide both numbers by 3:
\[ \frac{51 \div 3}{9 \div 3} = \frac{17}{3} \]
So, the ratio of females to males is \( 17:3 \).
Next, if 3 more males join the club, the number of males will increase to:
\[ 9 + 3 = 12 \]
The number of females remains the same at 51. Now we find the new ratio of females to males:
\[ \text{New ratio of females to males} = \frac{51}{12} \]
To simplify this ratio, we can find the greatest common divisor (GCD) of 51 and 12, which is 3:
\[ \frac{51 \div 3}{12 \div 3} = \frac{17}{4} \]
Therefore, the new ratio of females to males, after 3 more males join, is \( 17:4 \).