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 walked east for 15 2/3 meters from home, and west for 21 3/4 meters. To find how far Joey was from home, we need to find the difference between the two distances.
To add the mixed numbers, we need to convert them to improper fractions.
15 2/3 = (3 * 15 + 2) / 3 = 47/3
21 3/4 = (4 * 21 + 3) / 4 = 87/4
Now, the difference between the two distances is 87/4 - 47/3.
We need to find the least common multiple (LCM) of 3 and 4, which is 12.
Now, we need to convert the fractions to have the denominator of 12.
To do this, we need to multiply the numerator and the denominator by a number that will result in 12 as its denominator. For the first fraction, 3 is multiplied by 4, while for the second fraction, 4 is multiplied by 3.
87/4 * 3/3 = 261/12
47/3 * 4/4 = 188/12
Now, the difference between the two distances is 261/12 - 188/12 = 73/12.
So, Joey was 73/12 meters from home.
To determine how far Joey was from home, we need to find the difference between the distance he walked east and the distance he walked west.
The distance Joey walked east is 15 2/3 meters, and the distance he walked west is 21 3/4 meters.
To compare these distances, we can first convert the mixed numbers to improper fractions.
15 2/3 is equal to (3 * 15 + 2)/3 = 47/3
21 3/4 is equal to (4 * 21 + 3)/4 = 87/4
Now, let's find the difference between these two fractions.
47/3 - 87/4 = (47 * 4 - 87 * 3)/(3 * 4) = (188 - 261)/12 = -73/12
Therefore, Joey is 73/12 meters away from home.