## The operation of comparing fractions:

^{- 13}/_{100} vs. ^{- 17}/_{108}

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

#### - ^{13}/_{100} already reduced to the lowest terms;

the numerator and the denominator have no common prime factors:

13 is a prime number;

100 = 2^{2} × 5^{2};

#### - ^{17}/_{108} already reduced to the lowest terms;

the numerator and the denominator have no common prime factors:

17 is a prime number;

108 = 2^{2} × 3^{3};

## To sort fractions, build them up to the same numerator.

### Calculate LCM, the least common multiple of the numerators of the fractions

#### LCM will be the common numerator of the compared fractions.

#### The prime factorization of the numerators:

#### 13 is a prime number;

#### 17 is a prime number;

#### Multiply all the unique prime factors, by the largest exponents:

#### LCM (13, 17) = 13 × 17 = 221

### Calculate the expanding number of each fraction

#### Divide LCM by the numerator of each fraction:

#### For fraction: - ^{13}/_{100} is 221 ÷ 13 = (13 × 17) ÷ 13 = 17;

#### For fraction: - ^{17}/_{108} is 221 ÷ 17 = (13 × 17) ÷ 17 = 13;

### Expand the fractions

#### Build up all the fractions to the same numerator (which is LCM).

#### Multiply the numerators and the denominators by their expanding number:

#### - ^{13}/_{100} = - ^{(17 × 13)}/_{(17 × 100)} = - ^{221}/_{1,700};

#### - ^{17}/_{108} = - ^{(13 × 17)}/_{(13 × 108)} = - ^{221}/_{1,404};

### The fractions have the same numerator, compare their denominators.

#### The larger the denominator the larger the negative fraction.

## ::: Comparing operation :::

The final answer: