1 foot 4 inches = 1 foot * (12 inches)/(1 foot) + 4 inches = 16 inches
1 yard = (1 yard) * [(3 feet)/(1 yard)] * [(12 inches)/(1 foot)] = 36 inches
The ratio is: (16 inches)/(36 inches) = 16/36 = 4/9
(Note: the ratio has no units; it is expressed here as a fraction)