To solve the equation \( 110.16 : (24.6 \times x) = 1.8 \), we can first rewrite it for clarity:
\[ \frac{110.16}{24.6 \times x} = 1.8 \]
Next, we will multiply both sides by \( 24.6 \times x \):
\[ 110.16 = 1.8 \times (24.6 \times x) \]
Now, simplifying the right-hand side gives:
\[ 110.16 = 1.8 \times 24.6 \times x \]
Calculating \( 1.8 \times 24.6 \):
\[ 1.8 \times 24.6 = 44.088 \]
Now, we can substitute this back into the equation:
\[ 110.16 = 44.088 \times x \]
Next, divide both sides by \( 44.088 \) to solve for \( x \):
\[ x = \frac{110.16}{44.088} \]
Calculating the right side:
\[ x \approx 2.5 \]
Thus, the solution is:
\[ x \approx 2.5 \]