To find out how far Joey was from home, we need to find the difference between the distance he walked east and the distance he walked west.
Joey walked east for 15 2/3 meters.
Joey walked west for 21 3/4 meters.
To find the difference, we need to subtract 21 3/4 from 15 2/3.
To subtract mixed numbers, we need to first convert them into improper fractions.
To convert 15 2/3 to an improper fraction, we need to multiply the whole number (15) by the denominator (3) and then add the numerator (2). So, 15 2/3 is equal to (15 * 3 + 2)/3 = 47/3.
To convert 21 3/4 to an improper fraction, we need to multiply the whole number (21) by the denominator (4) and then add the numerator (3). So, 21 3/4 is equal to (21 * 4 + 3)/4 = 87/4.
Now, we can subtract the fractions: 47/3 - 87/4.
To subtract fractions, we need to have the same denominator. The least common multiple (LCM) of 3 and 4 is 12.
Converting 47/3 into a fraction with a denominator of 12:
(47/3) * (4/4) = 188/12.
Converting 87/4 into a fraction with a denominator of 12:
(87/4) * (3/3) = 261/12.
Now, we can subtract the fractions: 188/12 - 261/12 = -73/12.
So, Joey was -73/12 meters from home.
Since we are asked to write our answer as a mixed number, we need to convert the improper fraction -73/12 into a mixed number.
Dividing -73 by 12, we get -6 remainder 7.
Therefore, Joey was -6 7/12 meters from home.
In the context of the problem, being 6 7/12 meters from home means that Joey was 6 meters away in the opposite direction to home (in this case, west), and 7/12 of a meter further in that same direction. So, he was 6 7/12 meters from home.
Joey walked east for 15 2/3 meters from home. Then, walked west for 21 3/4 meters. How far was Joey from home? Write your answer as a mixed number only.
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