Question

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

(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?

A The 1,609 meters and the 804.5 meters in Step 1 should be switched.

B The 1 mile and 804.5 meters in Step 1 should be switched.

C The conversion factor should be added in Step 2 instead of being multiplied.

D The conversion factor should be divided in Step 2 instead of being multiplied

Answer 1

the best way to look at this is by writing it out.
\[\frac{1609 meters}{1}*\frac{1mile}{804.5meters}*\frac{1760yards}{1 mile}\]
the very left side should represent what you started with. writing it like this makes it easier to see the units crossed out.
can you see what is wrong with this?

Answer 2

Well, I don't know how to do any of this, but it seems that it'd be B, because the conversion factor usually is the denominator (1)