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.
To solve this problem, we need to find the difference between the distance Joey walked east and the distance he walked west.
Distance walked east = 15 2/3 meters
Distance walked west = 21 3/4 meters
To find the difference, we need to subtract the distance walked west from the distance walked east.
15 2/3 - (21 3/4)
First, let's find a common denominator for 3 and 4, which is 12.
Multiplying the numerator and denominator of 3/3 by 4, we get 12/12.
Multiplying the numerator and denominator of 4/4 by 3, we get 12/12.
Now the subtraction becomes:
15 8/12 - 21 9/12
Simplifying, we get:
15 8/12 - 21 9/12
= (15 - 21) + (8/12 - 9/12)
= -6 - 1/12
Since the result is negative, this means that Joey ended up west of his home.
Thus, Joey was 6 1/12 meters west of his home.
To find out how far Joey is from home, we need to subtract the distance he walked west from the distance he walked east.
Distance walked east: 15 2/3 meters
Distance walked west: 21 3/4 meters
To subtract these distances, we need to convert them to the same denominator.
To convert 15 2/3 to an improper fraction:
3 x 15 = 45
45 + 2 = 47
47/3 = 15 2/3
To convert 21 3/4 to an improper fraction:
4 x 21 = 84
84 + 3 = 87
87/4 = 21 3/4
Now, let's subtract the distances:
15 2/3 - 21 3/4
Since the denominators are already the same, we can subtract the whole numbers and the fractions separately:
15 - 21 = -6
2/3 - 3/4
The next step is to find a common denominator. The least common multiple of 3 and 4 is 12.
Converting 2/3 to twelfths:
3 x 4 = 12
2 x 4 = 8
8/12
Converting 3/4 to twelfths:
4 x 3 = 12
3 x 3 = 9
9/12
Now, let's subtract the fractions:
8/12 - 9/12
The denominators are the same, so we can subtract the numerators:
8 - 9 = -1
Combining the negative whole number and the negative fraction, we get -6 - 1/12.
Therefore, Joey is -6 1/12 meters away from home.
To find out 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. We can rewrite this as a mixed number by multiplying the whole number (15) by the denominator (3) and adding the numerator (2), and then placing this sum over the denominator: (15 * 3 + 2) / 3 = 47/3.
Joey walked west for 21 3/4 meters. Similarly, we can rewrite this as a mixed number: (21 * 4 + 3) / 4 = 87/4.
Now, to find out how far Joey is from home, we subtract the distance walked west from the distance walked east: 47/3 - 87/4.
To subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 4 is 12.
Now, we convert the two fractions so that they have a common denominator of 12:
(47/3) * (4/4) = 188/12
(87/4) * (3/3) = 261/12
Now, we subtract the two fractions: 188/12 - 261/12 = (188 - 261) / 12 = (-73) / 12.
Since the result is a negative number, it means Joey is 73/12 meters away from home in the west direction.
We can simplify this mixed number by dividing the numerator (-73) by the denominator (12): -73 ÷ 12 = -6 remainder -1.
So, Joey is 6 1/12 meters away from home in the west direction.