Joey walked east for 15 2/3 m from home then he walked west for 21 3/4 m. How far is Joey from home?
To find out how far Joey is from home, we need to subtract 21 3/4 m from 15 2/3 m.
First, let's rewrite the given distances as improper fractions:
15 2/3 m = 15 + 2/3 = 45/3 + 2/3 = 47/3 m
21 3/4 m = 21 + 3/4 = 84/4 + 3/4 = 87/4 m
Then, we can subtract those fractions:
47/3 m - 87/4 m = (47*4 - 87*3) / (3*4) = (188 - 261) / 12 = -73/12 m
Joey is 73/12 m away from home.
To find out how far Joey is from home, we need to calculate the total distance he traveled.
First, let's convert the mixed fractions to improper fractions:
15 2/3 = (3 * 15 + 2)/3 = 47/3
21 3/4 = (4 * 21 + 3)/4 = 87/4
Now we can add the distances traveled in each direction:
47/3 + 87/4
To add these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the fractions with a common denominator:
(47/3) * (4/4) = 188/12
(87/4) * (3/3) = 261/12
Adding the fractions:
188/12 + 261/12 = 449/12
So Joey is 449/12 m away from home.