Question

Joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was Joey from home?
Joey was meters from home.

Answer 1

To find the distance from home, we need to find the total displacement. Displacement is a vector quantity that tells us the change in position from the starting point to the ending point.

Joey walked east for 15 2/3 meters, which can be written as 15 + 2/3 = 15 2/3

Joey walked west for 21 3/4 meters, which can be written as 21 + 3/4 = 21 3/4

To find the total displacement, we need to subtract the westward displacement from the eastward displacement:

15 2/3 - 21 3/4

To subtract fractions, we need to find a common denominator. Since the denominator of 3/4 is 4, and the denominator of 2/3 is 3, the common denominator is 12.

Converting 2/3 to twelfths: 2/3 * 4/4 = 8/12
Converting 3/4 to twelfths: 3/4 * 3/3 = 9/12

Now we can subtract:
15 8/12 - 21 9/12 = 15 - 21 + 8/12 - 9/12 = -6 + (-1/12) = -6 1/12

So, Joey was 6 1/12 meters from home.