1 1/3 and 1 2/3; 1 1/10 and 1 13/30; 1 1/2 and 1 5/6; etc.
Explanation:
A mixed number is written as a whole number and a fraction, and it represents the sum of that whole number and fraction.
Starting at 0, the smallest mixed number would have to be over 1; this is because adding a fraction to 0 just gives us that fraction, not a mixed number using 0.
We want to use fractions that are 1/3 apart; the easiest to use is 1/3 and 2/3, giving us 1 1/3 and 1 2/3.
We can, however, also use other denominators. If we choose to use 1 1/10, we need to add 1/3 to this using a common denominator. The first number that both 10 and 3 will divide into evenly is 30. Changing the fractions, this gives us:
1 1/10 + 1/3 1 3/30 + 10/30 1 13/30
We can use the same process for 1 1/2 + 1/3; this time, the denominator will be 6: 1 1/2 + 1/3 1 3/6 + 2/6 1 5/6
