## The operation of comparing fractions:

^{- 139}/_{618} and ^{- 142}/_{628}

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

#### - ^{139}/_{618} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

139 is a prime number;

618 = 2 × 3 × 103;

#### - ^{142}/_{628} = - ^{(2 × 71)}/_{(22 × 157)} = - ^{((2 × 71) ÷ 2)}/_{((22 × 157) ÷ 2)} = - ^{71}/_{314}

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

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

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

#### The prime factorization of the numerators:

#### 139 is a prime number

#### 71 is a prime number

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

#### LCM (139, 71) = 71 × 139 = 9,869

### Calculate the expanding number of each fraction

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

#### For fraction: - ^{139}/_{618} is 9,869 ÷ 139 = (71 × 139) ÷ 139 = 71

#### For fraction: - ^{71}/_{314} is 9,869 ÷ 71 = (71 × 139) ÷ 71 = 139

### Expand the fractions

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

Multiply the numerators and denominators by their expanding number:

#### - ^{139}/_{618} = - ^{(71 × 139)}/_{(71 × 618)} = - ^{9,869}/_{43,878}

#### - ^{71}/_{314} = - ^{(139 × 71)}/_{(139 × 314)} = - ^{9,869}/_{43,646}

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

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

## ::: Comparing operation :::

The final answer: