joey walks east for 15 2/3 meter from home then he walked west for 21 3/4
To find out how far Joey is from home after walking east for 15 2/3 meters, we subtract this distance from his starting point. Start with the whole number part:
15 meters - 0 meters = 15 meters
Now, let's subtract the fractional part:
2/3 meter
Since 1 meter is divided into 3 equal parts, we can divide it into thirds. Two-thirds of a meter is less than 1 meter, so it will take us closer to zero meters. Subtract 2/3 meter from 15 meters:
15 - 2/3 = (15 * 3) / 1 - 2/3 = 45/1 - 2/3 = 45/1 - 2 * 3 / 3 = 45/1 - 6/3 = 45/1 - 6/3 = 45/1 - 2 = 45 - 2 = 43
So, Joey is 43 meters from home after walking east for 15 2/3 meters.
Now, let's find out how far Joey is from home after walking west for 21 3/4 meters. Subtract this distance from his current location:
43 meters - 21 meters = 22 meters
Now, we need to consider the fractional part:
3/4 meter
Since 1 meter is divided into 4 equal parts, we can divide it into quarters. Three-quarters of a meter is less than 1 meter, so it will take us closer to zero meters. Subtract 3/4 meter from 22 meters:
22 - 3/4 = (22 * 4) / 1 - 3/4 = 88/1 - 3/4 = 88/1 - 3 * 4 / 4 = 88/1 - 12/4 = 88/1 - 12/4 = 88/1 - 3 = 88 - 3 = 85
Therefore, Joey is 85 meters from home after walking west for 21 3/4 meters.
To find out where Joey is after walking east and then west, we need to calculate the total displacement.
Step 1: 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
Step 2: Subtract the west displacement (87/4) from the east displacement (47/3).
(47/3) - (87/4) = (47/3) + (-87/4) (since subtracting is the same as adding the opposite)
Step 3: Find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
LCM(3, 4) = 12
Step 4: Convert the fractions to have a common denominator of 12.
(47/3) + (-87/4) = (47/3) * (4/4) + (-87/4) * (3/3)
= (188/12) + (-261/12)
Step 5: Combine the numerators and keep the common denominator.
(188/12) + (-261/12) = (188 - 261) / 12
= -73/12
Joey is -73/12 meters from home in the west direction.