Question

The steps below show the work of a student used to calculate the number of yards in 804.5 meters.

Answer 1

(1 mile = 1,609 meters)
(1 mile = 1,760 yards)

Step 1: 1,609 meters is being multiplied by conversion factor 1 mile over 804.5 meters equals 2 miles

Step 2: 2 miles is being multiplied by conversion factor 1760 yards over 1 mile equals 3,520 yards

Step 3: 3,520 yards
(1 mile = 1,609 meters)
(1 mile = 1,760 yards)

How can the error in the student's work be corrected?

Answer 2

because 1 mile = 1609 meters, the conversion factor is 1 mile/1609 meters, not 1 mile/804.5 meters.

the proper setup for step 1 is: 804.5 meters * (1 mile / 1609 meters)

additionally, for step 2, the conversion factor is 1760 yards/ 1 mile since we're in miles at this point.