To find out how far Joey was from home after his walk, we need to combine the distances he walked in both directions.
- Joey walked 15 2/3 meters east.
- Then he walked 21 3/4 meters west.
First, let's convert both mixed numbers to improper fractions:
- \(15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}\)
- \(21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}\)
Next, we need to find a common denominator to perform the subtraction. The least common multiple (LCM) of 3 and 4 is 12.
Now, let's convert both fractions to have a denominator of 12:
-
For \(\frac{47}{3}\): \[ \frac{47 \times 4}{3 \times 4} = \frac{188}{12} \]
-
For \(\frac{87}{4}\): \[ \frac{87 \times 3}{4 \times 3} = \frac{261}{12} \]
Now we can subtract the distances:
\[ \text{Distance from home} = \frac{261}{12} - \frac{188}{12} = \frac{261 - 188}{12} = \frac{73}{12} \]
To convert \(\frac{73}{12}\) to a mixed number: Divide 73 by 12:
- \(73 \div 12 = 6\) remainder \(1\), so: \[ \frac{73}{12} = 6 \frac{1}{12} \]
Thus, after walking, Joey is \(6 \frac{1}{12}\) meters from home to the west.