How do I multiply two measurements of feet and inches to get exact square footage?

Example: 5' 12", 6' 1" (picked stupid easy numbers)

1) Multiple the feet terms: 5 * 6 = 30 sqft
2) Multiply the inch terms: 12 * 1 = 12 sq inches
3) Convert inches to feet by the conversion 12"/1' X 12"/1' = 144 sqin/1sqft
4) 12 sqin * 1sqft/144 sq in; check dimensionally so it works out in sq ft.
5) Add 30 sqft + 12/144 sqft

6) Get it in the form of 30.xyz or whatever sqft or simplify the fraction

Yep. Wrong answer.

Easiest way is to convert the two measurements into inches, multiply them together, then divide by 144 sq in/sq ft to get it into square feet.

Example: consider a room that is 10'5" long by 8'9" wide. This converts to:

length: 10 ft * 12 in/ft + 5 = 125 inches.
width: 8*12+9 = 105 inches

Area = length * width = 125 inches * 105 inches = 13125 sq inches.

13125 sq inches/144 = 91.14 sq ft.