A job is shared by 4 workers, W, X, Y, and Z. Worker W does 1/4 of the total hours. Worker X does 1/3 of the total hours. Worker Y does 1/6 of the total hours. What fraction represents the remaining hours allocated to person Z?
1/4
1/4 + 1/3 + 1/6
3/12 + 4/12 + 2/12 = 9/12 = 3/4
4/4 - 3/4 = ?
To find the fraction representing the remaining hours allocated to person Z, we need to determine the fractions of hours worked by workers W, X, and Y, and subtract the sum of those fractions from 1 (since all workers together account for the entire job).
Worker W does 1/4 of the total hours, so the fraction of hours worked by W is 1/4.
Worker X does 1/3 of the total hours, so the fraction of hours worked by X is 1/3.
Worker Y does 1/6 of the total hours, so the fraction of hours worked by Y is 1/6.
Adding these fractions together:
1/4 + 1/3 + 1/6 = 12/24 + 8/24 + 4/24 = 24/24
Since the sum of these fractions is equal to 1, the remaining hours allocated to person Z is:
1 - 1 = 0.
Therefore, the fraction representing the remaining hours allocated to person Z is 0.
To find the fraction representing the remaining hours allocated to person Z, we need to find the sum of the fractions worked by workers W, X, and Y, and subtract it from 1 (as the total fraction of work is equal to 1).
Let's calculate the fractions worked by each worker:
Worker W does 1/4 of the total hours.
Worker X does 1/3 of the total hours.
Worker Y does 1/6 of the total hours.
To find the sum of these fractions, we'll find a common denominator:
First, we'll find the least common multiple (LCM) of 4, 3, and 6:
The multiples of 4 are: 4, 8, 12, 16, 20, ...
The multiples of 3 are: 3, 6, 9, 12, 15, 18, ...
The multiples of 6 are: 6, 12, 18, 24, ...
From this list, we can see that the LCM of 4, 3, and 6 is 12.
Now, let's express the fractions with the common denominator of 12:
Worker W: (1/4) * (3/3) = 3/12
Worker X: (1/3) * (4/4) = 4/12
Worker Y: (1/6) * (2/2) = 2/12
Now, we can find the sum of these fractions:
3/12 + 4/12 + 2/12 = 9/12
Finally, to find the remaining fraction allocated to person Z, we subtract this sum from 1:
1 - 9/12 = 12/12 - 9/12 = 3/12
So, the fraction representing the remaining hours allocated to person Z is 3/12.