Explanation:
16 3/4 days in total.
that are (16×4 + 3)/4 = 67/4 days.
he has taken
1 3/4 = (1×4 + 3)/4 = 7/4 days
4 2/3 = (4×3 + 2)/3 = 14/3 days
2 1/6 = (2×6 + 1) = 13/6 days
to be able to add abd subtract them directly, we need to bring all fractions to the same denominator.
we have 3, 4, 6 : the smallest common multiple is 12 (can be divided without remainder by 3, 4 and 6).
we need to multiply each fraction by a fitting n/n factor to bring the denominators to 12 and keep the overall value of the fraction unchanged.
67/4 = 67/4 × 3/3 = 201/12
7/4 = 7/4 × 3/3 = 21/12
14/3 = 14/3 × 4/4 = 56/12
13/6 = 13/6 × 2/2 = 26/12
the remaining vacation time is
201/12 - 21/12 - 56/12 - 26/12 = 98/12 = 49/6
49/6 = 8 and remainder 1 = (8×6 + 1)/6 = 8 1/6 days