Joey walk East four 15 2/3 m of home then he walked west for 21 3/4 m. How far is Julie from home?
Solve step by step
To solve this problem, we can start by finding the total distance Joey walked.
First, we need to convert the mixed numbers to improper fractions. We have 2/3 m and 3/4 m.
2/3 can be converted to an improper fraction by multiplying the whole number (4) by the denominator and adding the numerator. So, 4 * 3 + 2 = 14/3 m.
3/4 can be converted to an improper fraction by multiplying the whole number (21) by the denominator and adding the numerator. So, 21 * 4 + 3 = 87/4 m.
Next, we can add the two distances: 14/3 m + 87/4 m.
To add these fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12.
To convert 14/3 to have a denominator of 12, we multiply the numerator and denominator by 4: (14 * 4) / (3 * 4) = 56/12 m.
To convert 87/4 to have a denominator of 12, we multiply the numerator and denominator by 3: (87 * 3) / (4 * 3) = 261/12 m.
Now we can add the two fractions: 56/12 m + 261/12 m = (56 + 261) / 12 m = 317/12 m.
Therefore, Joey walked a total of 317/12 m.
However, the question asks for how far Julie is from home, not how far Joey walked.
Since Joey walks east 15 2/3 m and then walks west 21 3/4 m, we can subtract the distance Joey walked west from the distance he walked east to find Julie's distance from home.
15 2/3 m - 21 3/4 m can be solved by converting the mixed numbers to improper fractions.
15 2/3 can be converted to an improper fraction: 3 * 15 + 2 = 47/3 m.
21 3/4 can be converted to an improper fraction: 4 * 21 + 3 = 87/4 m.
Now we can subtract the two fractions: 47/3 m - 87/4 m.
To subtract fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12.
To convert 47/3 to have a denominator of 12, we multiply the numerator and denominator by 4: (47 * 4) / (3 * 4) = 188/12 m.
To convert 87/4 to have a denominator of 12, we multiply the numerator and denominator by 3: (87 * 3) / (4 * 3) = 261/12 m.
Now we can subtract the two fractions: 188/12 m - 261/12 m = (188 - 261) / 12 m = -73/12 m.
Therefore, Julie is 73/12 m away from home.
1. Joey walked east for 15 2/3 m. Convert the mixed fraction to an improper fraction: 15 2/3 = (3 * 15 + 2) / 3 = 47/3 m.
2. Joey then walked west for 21 3/4 m. Convert the mixed fraction to an improper fraction: 21 3/4 = (4 * 21 + 3) / 4 = 87/4 m.
3. Calculate the difference between Joey's east and west distances: 47/3 - 87/4.
To find the common denominator, we multiply the denominators: 3 * 4 = 12.
4. Adjust the fractions with the common denominator:
(47/3) * (4/4) = 188/12, and (87/4) * (3/3) = 261/12.
5. Calculate the difference: 188/12 - 261/12 = -73/12.
6. The negative sign indicates that Joey is west of the starting point.
7. Simplify the fraction: -73/12 cannot be simplified further.
So, Julie is 73/12 m west of home.