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? Write your answer as a mixed number only
To find the distance, we need to subtract the distance Joey walked west from the distance Joey walked east.
Distance = (15 2/3) - (21 3/4)
First, let's convert the mixed numbers into improper fractions.
15 2/3 = (3 * 15 + 2) / 3 = (45 + 2) / 3 = 47 / 3
21 3/4 = (4 * 21 + 3) / 4 = (84 + 3) / 4 = 87 / 4
Now we can substitute these values back into the equation.
Distance = (47/3) - (87/4)
To subtract fractions, we need to have a common denominator.
The least common multiple of 3 and 4 is 12.
Distance = (47/3)(4/4) - (87/4)(3/3)
Distance = 188/12 - 261/12
Now we can subtract.
Distance = (188 - 261) / 12
Distance = -73 / 12
The distance Joey was from home was -73/12 meters.
To find the distance from home, we can subtract the distance walked west from the distance walked east.
Distance walked east: 15 2/3 meters
Distance walked west: 21 3/4 meters
To subtract these distances, we need to find a common denominator for 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.
Converting both fractions to twelfths:
15 2/3 = 15 * 3/3 + 2/3 = 45/3 + 2/3 = 47/3 (meters)
21 3/4 = 21 * 3/4 + 3/4 = 63/4 + 3/4 = 66/4 (meters)
Now, we can subtract:
47/3 - 66/4 = (47 * 4)/(3 * 4) - 66/4 = 188/12 - 66/4 = 188/12 - 198/12 = (188 - 198)/12 = -10/12
So, Joey is -10/12 meters from home.
However, a negative distance doesn't make sense in this context, so we should consider Joey as being 10/12 meters away from home in the opposite direction.
Simplifying the fraction:
-10/12 = (-1 * 10)/(2 * 6) = -10/12 = -5/6
Therefore, Joey is 5/6 meters away from home in the opposite direction.