Joey walked east for 152/3 meters from home. Then, he walked west for 213/4 meters. How far was Joey from home?
To solve this problem, we need to calculate the absolute difference between the distances Joey walked east and west.
152/3 meters is equivalent to 50 2/3 meters.
213/4 meters is equivalent to 53 1/4 meters.
To find the absolute difference, we subtract the smaller distance from the larger distance:
53 1/4 - 50 2/3 = 53 1/4 - 50 4/6
53 1/4 - 50 4/6 = 53 1/4 - ( 50 * 6 + 4)/6
53 1/4 - 50 4/6 = 53 1/4 - 304/6
53 1/4 - 304/6 = (53 * 4 + 1)/4 - 304/6
53 1/4 - 304/6 = 212 + 1) / 4 - 304/6
53 1/4 - 304/6 = 213/4 - 304/6
53 1/4 - 304/6 = (213 * 6 - 304 * 4)/(24)
53 1/4 - 304/6 = (1278 - 1216)/(24)
53 1/4 - 304/6 = 62/24
Thus, Joey was 62/24 meters or 2 5/12 meters from home.
To find out how far Joey was from home, we need to calculate the total distance he walked in each direction and then find the net distance from home.
First, let's calculate the total distance Joey walked east:
152/3 meters
Next, let's calculate the total distance Joey walked west:
213/4 meters
To find the net distance from home, we need to subtract the distance walked west from the distance walked east:
152/3 - 213/4
To subtract these fractions, we need to find a common denominator:
The least common multiple (LCM) of 3 and 4 is 12.
Let's convert the fractions to have a denominator of 12:
152/3 = (152/3) * (4/4) = 608/12
213/4 = (213/4) * (3/3) = 639/12
Now we can subtract the fractions:
608/12 - 639/12 = (608 - 639)/12 = -31/12
The negative sign indicates that Joey ended up 31/12 meters to the west of his starting point.
Therefore, Joey was 31/12 meters from home.