No one third is smaller than two third.
One third is 1/3 and two third is 2/3.
Since the denominator (which is 3 in this case) are the same, we will need to look at the numerators (which is 1 and 2 respectivelty in this case). If the denominator are the same for two fractions, the fraction with the larger numerator will be the larger number.
Since 2 is greater than 1, in this case, 2/3 is the larger number.
As for the symbols, > means greater than and < means less than.