Question

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.

Answer 1

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.