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.(1 point)
Joey was
meters from home.
To find Joey's distance from home, we need to subtract the westward distance from the eastward distance.
The eastward distance is 15 2/3 meters.
The westward distance is 21 3/4 meters.
To subtract these distances, we need to find a common denominator for the fractions. The smallest common denominator for 3 and 4 is 12.
15 2/3 = 15 * 3/3 + 2/3 = 45/3 + 2/3 = 47/3
21 3/4 = 21 * 4/4 + 3/4 = 84/4 + 3/4 = 87/4
Now, we can subtract:
47/3 - 87/4
To get a common denominator, we multiply 3 by 4 to get 12:
(47/3) * (4/4) - 87/4
Now, we can subtract the fractions:
(47 * 4) / 12 - 87/4
188/12 - 87/4
To have the same denominator, we multiply 188/12 by 1 in the form of 4/4:
(188/12) * (4/4) - 87/4
Now we can subtract:
(752/48) - 87/4
Final step: subtract the fractions:
752/48 - 87/4 = (752 - 1056)/48 = -304/48 = -19/3
Since Joey walked in the opposite direction, we take the absolute value of the result:
|-19/3| = 19/3 = 6 1/3
Therefore, Joey was 6 1/3 meters from home.
To determine how far Joey is from home, we need to subtract the distance he walked west from the distance he walked east.
Joey walked east for 15 2/3 meters.
Joey walked west for 21 3/4 meters.
To subtract these values, we need to find a common denominator for the fractions.
The denominators are 3 and 4. The least common multiple of 3 and 4 is 12.
Converting the fractions to have a denominator of 12:
15 2/3 = 15 * 3/3 + 2/3 = 45/3 + 2/3 = 47/3
21 3/4 = 21 * 4/4 + 3/4 = 84/4 + 3/4 = 87/4
Now, we can subtract:
47/3 - 87/4
To subtract fractions with different denominators, we need to get a common denominator. In this case, the common denominator is 3 * 4 = 12.
47/3 = 47 * 4/3 * 4 = 188/12
87/4 = 87 * 3/4 * 3 = 261/12
Now, we can do the subtraction:
188/12 - 261/12 = (188 - 261)/12 = -73/12
Therefore, Joey is -73/12 meters from home.
However, since we need the answer as a mixed number, we can simplify this fraction.
Dividing -73 by 12 gives us a quotient of -6 with a remainder of 7.
So, Joey is -6 and 7/12 meters from home.
Note: The negative sign indicates that Joey is west of his starting point.