To find the ratio of the number of sundaes without nuts to the number of sundaes with nuts, we have the following numbers:
- Number of sundaes without nuts: 18
- Number of sundaes with nuts: 32
The ratio is calculated as follows:
\[ \text{Ratio} = \frac{\text{Number of sundaes without nuts}}{\text{Number of sundaes with nuts}} = \frac{18}{32} \]
Next, we can simplify this fraction. Both 18 and 32 can be divided by their greatest common divisor (GCD), which is 2:
\[ \frac{18 \div 2}{32 \div 2} = \frac{9}{16} \]
Thus, the ratio of the number of sundaes without nuts to the number of sundaes with nuts is \( \frac{9}{16} \).
In conclusion, the final ratio is:
\[ \boxed{9:16} \]
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