## The operation of sorting fractions in ascending order:

^{1}/_{10}, ^{5}/_{6}, ^{2}/_{6}, ^{1}/_{3}

### Analyze the fractions to be compared and ordered, by category:

#### positive proper fractions: ^{1}/_{10}, ^{5}/_{6}, ^{2}/_{6}, ^{1}/_{3};

### Reduce (simplify) fractions to their lowest terms equivalents:

^{1}/_{10} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

1 cannot be factored into other prime factors;

10 = 2 × 5;

^{5}/_{6} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

5 is a prime number;

6 = 2 × 3;

^{2}/_{6} = ^{2}/_{(2 × 3)} = ^{(2 ÷ 2)}/_{((2 × 3) ÷ 2)} = ^{1}/_{3}

^{1}/_{3} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

1 cannot be factored into other prime factors;

3 is a prime number;