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? Show your work.
To solve this problem, we need to find the total distance from Joey's starting point to his ending point.
To find the total distance, we find the sum of the distances traveled east and west.
Distance traveled east: 15 2/3 meters
= 15 + 2/3 meters
= 45/3 + 2/3 meters
= 47/3 meters
Distance traveled west: 21 3/4 meters
= 21 + 3/4 meters
= 84/4 + 3/4 meters
= 87/4 meters
Total distance from home = Distance traveled east - Distance traveled west
= 47/3 - 87/4
To subtract the fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12.
47/3 = 15 2/3 * 4/4 = 60/12
87/4 = 21 3/4 * 3/3 = 261/12
Total distance from home = (60/12) - (261/12)
= -201/12
Since the value is negative, it means that Joey is 201/12 meters away from home in the west direction.
Thus, Joey is 201/12 meters away from home.
To find out how far Joey is from home, we will use the concept of adding and subtracting fractions.
First, let's convert the mixed numbers to improper fractions:
15 2/3 = (3 * 15 + 2)/3 = 47/3
21 3/4 = (4 * 21 + 3)/4 = 87/4
Now, subtract the distances Joey walked west from the distance he walked east:
47/3 - 87/4
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 12:
(47/3) * (4/4) - (87/4) * (3/3)
= 188/12 - 261/12
Now, subtract the numerators:
188/12 - 261/12 = (188 - 261)/12 = -73/12
So, Joey is -73/12 meters away from home.
Note: The negative sign indicates that Joey is west of his starting point.