To write the ratio of 20 inches to 3 feet in fractional notation and simplify it to lowest terms, we first convert feet to inches.
Since 1 foot = 12 inches, we can convert 3 feet to inches: \[ 3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches} \]
Now, we can write the ratio of 20 inches to 36 inches as a fraction: \[ \frac{20}{36} \]
Next, we simplify the fraction. Both the numerator and the denominator can be divided by their greatest common divisor, which is 4: \[ \frac{20 \div 4}{36 \div 4} = \frac{5}{9} \]
Thus, the simplified ratio of 20 inches to 3 feet is: \[ \frac{5}{9} \]
So the correct response is: Start fraction 5 over 9 end fraction.