Each of the problems asks you to a similar idea: get a common denominator with the fractions and then subtract.
Problem 1: 28 3/8 - 19 5/6
The factors of 8 are 2, 2, and 2. The factors of 6 are 2 and 3. We take one two that's repeated, two more twos from 8, and a 3 for the common denominator. So, 2 * 2 * 2 * 3 = 24 is the lowest common denominator (LCD).
Now change the fractions to the common denominators
3/8 = ? / 24 We go from 8 to 24 multiplying by 3, so 3 multiplied by 3 is 9.
5/6 = ? / 24 We go from 6 to 24 multipling by 4, so 5 multiplied by 4 is 20.
Then,
28 3/8 - 19 5/6
= 28 9/24 - 19 20/24 <----use common denominators
= 27 33/24 - 19 20/24 <--- borrow from the whole number
= 8 13/24 <---- subtract whole numbers and fraction numerators
Problem 2 works similarly to problem 1, with an LCD of 15.
18 2/5 - 9 13/15
= 18 6/15 - 9 13/15
= 17 21/15 - 9 13/15
= 8 8/15
Thus the differences are 8 13/24 (1st) and 8 8/15 (2nd).
