## The operation of comparing fractions:

^{- 138}/_{146} and ^{- 141}/_{150}

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

#### - ^{138}/_{146} = - ^{(2 × 3 × 23)}/_{(2 × 73)} = - ^{((2 × 3 × 23) ÷ 2)}/_{((2 × 73) ÷ 2)} = - ^{69}/_{73}

#### - ^{141}/_{150} = - ^{(3 × 47)}/_{(2 × 3 × 52)} = - ^{((3 × 47) ÷ 3)}/_{((2 × 3 × 52) ÷ 3)} = - ^{47}/_{50}

## 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:

#### 69 = 3 × 23

#### 47 is a prime number

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

#### LCM (69, 47) = 3 × 23 × 47 = 3,243

### Calculate the expanding number of each fraction

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

#### For fraction: - ^{69}/_{73} is 3,243 ÷ 69 = (3 × 23 × 47) ÷ (3 × 23) = 47

#### For fraction: - ^{47}/_{50} is 3,243 ÷ 47 = (3 × 23 × 47) ÷ 47 = 69

### Expand the fractions

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

Multiply the numerators and denominators by their expanding number:

#### - ^{69}/_{73} = - ^{(47 × 69)}/_{(47 × 73)} = - ^{3,243}/_{3,431}

#### - ^{47}/_{50} = - ^{(69 × 47)}/_{(69 × 50)} = - ^{3,243}/_{3,450}

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

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

## ::: Comparing operation :::

The final answer: