5 1/6 - 1 1/2 - 1 7/9

To subtract mixed numbers, we need to first convert them to improper fractions.

5 1/6 = 31/6
1 1/2 = 3/2
1 7/9 = 16/9

Now we can subtract:

31/6 - 3/2 - 16/9

To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is the least common multiple (LCM) of 6, 2, and 9, which is 18.

Now we need to express each fraction with the common denominator:

31/6 = (31/6) * (3/3) = 93/18
3/2 = (3/2) * (9/9) = 27/18
16/9 = (16/9) * (2/2) = 32/18

Now we can subtract the fractions:

93/18 - 27/18 - 32/18 = (93 - 27 - 32)/18 = 34/18

We can simplify the fraction:

34/18 = (2*17)/(2*9) = 17/9

The result of the subtraction is 17/9.