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.
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.
To find out how far Joey was from home, we need to subtract the distance he walked west from the distance he walked east.
Joey walked east for 15 2/3 meters and west for 21 3/4 meters.
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 two distances:
47/3 - 87/4
To subtract fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.
So, let's rewrite the fractions with the common denominator of 12:
(47/3)(4/4) - (87/4)(3/3)
This gives us:
(188/12) - (261/12)
Now, subtract the numerators:
188 - 261 = -73
So, Joey was -73/12 meters from home.
However, distance is a positive value, so we'll take the absolute value:
|-73/12| = 73/12
Therefore, Joey was 73/12 meters from home.
To find out how far Joey was from home, we need to subtract the distance he walked west from the distance he walked east.
Joey walked east for 15 2/3 meters, which can be written as an improper fraction: 15 + 2/3 = 45/3 + 2/3 = 47/3 meters.
Joey walked west for 21 3/4 meters, which can also be written as an improper fraction: 21 + 3/4 = 84/4 + 3/4 = 87/4 meters.
To subtract these two distances, we need to have a common denominator. In this case, the lowest common multiple of 3 and 4 is 12.
Converting the fractions to have a denominator of 12:
47/3 * 4/4 = 188/12
87/4 * 3/3 = 261/12
Now we can subtract:
188/12 - 261/12 = -73/12
The answer is -73/12 meters, which means Joey is 73/12 meters to the west of his home.