Question

Question #a5ac3

Answer 1

The third worker should budget `1/6` of their time

Explanation:

The three fractions of the three people's workloads should add to 1, which we can write as `1/1`

so `1/2 + 1/3 + "third workload = 1/1"`

`"third workload" = 1/1 - 1/2 - 1/3`
Since the denominators are different, we need to make them the same by multiplying the numerator and denominator of each fraction. We can do this by finding the lowest common multiple of all the denominators.
The lowest number that 1, 2, 3 and all multiply into is `6`, so that is what the new denominator should be.

if we multiply `1/2` by `3/3` we get `3/6`, which has the denominator we want

if we multiply `1/3` by `2/2` we get `2/6`, which has the denominator we want

if we multiply `1/1` by `6/6` we get `6/6`, which has the denominator we want

The values of the fractions have not changed since `3/3`, `2/2`, and `6/6` all are equal to one, and multiplying by one does not change the value of a number

then we simply use these new fractions in place of the old ones in the equation

`"third workload" = 6/6 - 3/6 - 2/6`

`"third workload" = 1/6`

So the third worker should budget `1/6` of their time