Which set of mixed numbers has a difference less than one?

Let's calculate the difference for each set of mixed numbers:

A. 1 and 2/9 x 1 and 1/9:
To subtract mixed numbers, we first need to convert them into improper fractions.
1 and 2/9 is equal to (9 * 1 + 2) / 9 = 11/9.
1 and 1/9 is equal to (9 * 1 + 1) / 9 = 10/9.

Now, subtracting the two improper fractions:
11/9 - 10/9 = (11 - 10) / 9 = 1/9.

B. 3 and 4/7 x 2 and 1/7:
3 and 4/7 is equal to (7 * 3 + 4) / 7 = 25/7.
2 and 1/7 is equal to (7 * 2 + 1) / 7 = 15/7.

Subtracting the two improper fractions:
25/7 - 15/7 = (25 - 15) / 7 = 10/7 = 1 and 3/7.

C. 2 and 4/5 x 1 and 1/3:
2 and 4/5 is equal to (5 * 2 + 4) / 5 = 14/5.
1 and 1/3 is equal to (3 * 1 + 1) / 3 = 4/3.

Subtracting the two improper fractions:
14/5 - 4/3 = [(14 * 3) - (4 * 5)] / (5 * 3) = (42 - 20) / 15 = 22/15.

D. 2 and 7/9 x 1 and 1/3:
2 and 7/9 is equal to (9 * 2 + 7) / 9 = 25/9.
1 and 1/3 is equal to (3 * 1 + 1) / 3 = 4/3.

Subtracting the two improper fractions:
25/9 - 4/3 = [(25 * 3) - (4 * 9)] / (9 * 3) = (75 - 36) / 27 = 39/27.

Comparing the results:
A. 1/9
B. 1 and 3/7
C. 22/15
D. 39/27

Based on the results, the only set that has a difference less than one is option A, 1 and 2/9 x 1 and 1/9.