\( \frac { 20 } { \square } = \frac { 30 } { 81 } = \frac { \square } { 108 } \)

To solve this problem, we need to find the missing numbers in the equation. We have three fractions that are equal to each other: \[ \frac{20}{\square} = \frac{30}{81} = \frac{\square}{108} \] First, let's find the missing number in the first fraction by setting the two equal fractions equal to each other: \[ \frac{20}{\square} = \frac{30}{81} \] To find the missing denominator, we can cross-multiply: \[ 20 \times 81 = 30 \times \square \] \[ 1620 = 30 \times \square \] Now, divide both sides by 30 to solve for the missing denominator: \[ \square = \frac{1620}{30} \] \[ \square = 54 \] So the first fraction is: \[ \frac{20}{54} \] Now, let's find the missing number in the third fraction by setting the two equal fractions equal to each other: \[ \frac{30}{81} = \frac{\square}{108} \] Again, we cross-multiply: \[ 30 \times 108 = 81 \times \square \] \[ 3240 = 81 \times \square \] Now, divide both sides by 81 to solve for the missing numerator: \[ \square = \frac{3240}{81} \] \[ \square = 40 \] So the third fraction is: \[ \frac{40}{108} \] To summarize, the missing numbers are 54 and 40. The complete equation is: \[ \frac{20}{54} = \frac{30}{81} = \frac{40}{108} \]