To express the ratio \(20\) inches to \(3\) feet using fractional notation, we first need to convert the feet to inches. Since \(1\) foot is equal to \(12\) inches, we have:
\[ 3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches} \]
Now, we can write the ratio of \(20\) inches to \(36\) inches as a fraction:
\[ \text{Ratio} = \frac{20 \text{ inches}}{36 \text{ inches}} \]
Next, we simplify the fraction:
\[ \frac{20}{36} \]
To simplify, we find the greatest common divisor (GCD) of \(20\) and \(36\). The GCD is \(4\), so we divide both the numerator and the denominator by \(4\):
\[ \frac{20 \div 4}{36 \div 4} = \frac{5}{9} \]
Thus, the simplified ratio of \(20\) inches to \(3\) feet is:
\[ \frac{5}{9} \]
The correct answer is \(\frac{5}{9}\).
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