## The operation of comparing fractions:

^{- 150}/_{180} and ^{- 155}/_{183}

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

#### - ^{150}/_{180} = - ^{(2 × 3 × 52)}/_{(22 × 32 × 5)} = - ^{((2 × 3 × 52) ÷ (2 × 3 × 5))}/_{((22 × 32 × 5) ÷ (2 × 3 × 5))} = - ^{5}/_{6}

#### - ^{155}/_{183} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

155 = 5 × 31;

183 = 3 × 61;

## 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:

#### 5 is a prime number

#### 155 = 5 × 31

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

#### LCM (5, 155) = 5 × 31 = 155

### Calculate the expanding number of each fraction

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

#### For fraction: - ^{5}/_{6} is 155 ÷ 5 = (5 × 31) ÷ 5 = 31

#### For fraction: - ^{155}/_{183} is 155 ÷ 155 = (5 × 31) ÷ (5 × 31) = 1

### Expand the fractions

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

Multiply the numerators and denominators by their expanding number:

#### - ^{5}/_{6} = - ^{(31 × 5)}/_{(31 × 6)} = - ^{155}/_{186}

#### - ^{155}/_{183} = - ^{(1 × 155)}/_{(1 × 183)} = - ^{155}/_{183}

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

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

## ::: Comparing operation :::

The final answer: