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.
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.
To determine how far Joey is from home, we need to subtract the distance he walked to the west from the distance he walked to the east.
First, convert the mixed numbers to improper fractions:
Distance walked east: 15 2/3 = (3 * 15 + 2) / 3 = 47/3
Distance walked west: 21 3/4 = (4 * 21 + 3) / 4 = 87/4
Now, subtract 87/4 from 47/3:
47/3 - 87/4
To perform this subtraction, we need to find a common denominator:
The least common multiple (LCM) of 3 and 4 is 12.
Multiply the numerator and denominator of the first fraction (47/3) by 4:
(47 * 4) / (3 * 4) = 188/12
Multiply the numerator and denominator of the second fraction (87/4) by 3:
(87 * 3) / (4 * 3) = 261/12
Subtract the two fractions:
188/12 - 261/12 = (188 - 261) / 12 = -73/12
The distance Joey is from home is -73/12 meters.
However, since distance cannot be negative, we express it as a positive mixed number:
Divide the numerator (-73) by the denominator (12) to get the whole number part:
-73 ÷ 12 = -6 remainder 5
The whole number part is -6. The remainder (5) is the new numerator, and the denominator (12) remains the same.
Therefore, the distance Joey is from home is:
-6 5/12 meters
But since we are asked to write our answer as a mixed number only, the final answer is:
-6 5/12 meters