Question

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

Step 1: 1,609 meters is being multiplied by the conversion factor 1 mile over 804.5 meters equals 2 miles
Step 2: 2 miles is being multiplied by the conversion factor 1,760 yards over 1 mile equals 3,520 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 student's error can be corrected by accurately applying the conversion factors. In step 1, switch the places of 1 mile and 804.5 meters to find the number of miles and then in step 2, multiply by the conversion factor of 1760 yards in a mile to convert the result to yards.

Step-by-step explanation:

To correct the error in the student's calculation of the number of yards in 804.5 meters, the conversion factors used in each step need to be correctly applied. Starting with meters, we know that the conversion factor for meters to miles should be that 1 mile is equal to 1609.34 meters. Hence, in step 1, we use this conversion by dividing 804.5 meters by 1609.34 meters per mile to find the number of miles. The correct calculation would be:

804.5 meters × (1 mile / 1609.34 meters) = 0.5 miles (approximately)

In Step 2, to convert miles to yards, we know that there are 1760 yards in 1 mile. So, we should multiply the number of miles by this factor:

0.5 miles × (1760 yards / 1 mile) = 880 yards

Therefore, the answer to how the error can be corrected is:

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