## The operation of comparing fractions:

^{- 98}/_{60} and ^{- 108}/_{68}

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

#### - ^{98}/_{60} = - ^{(2 × 72)}/_{(22 × 3 × 5)} = - ^{((2 × 72) ÷ 2)}/_{((22 × 3 × 5) ÷ 2)} = - ^{49}/_{30}

#### - ^{108}/_{68} = - ^{(22 × 33)}/_{(22 × 17)} = - ^{((22 × 33) ÷ 22)}/_{((22 × 17) ÷ 22)} = - ^{27}/_{17}

## To sort fractions in ascending order, build up their denominators the same.

### Calculate LCM, the least common multiple of the denominators of the fractions.

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

In this case, LCM is also called LCD, the least common denominator.

#### The prime factorization of the denominators:

#### 30 = 2 × 3 × 5

#### 17 is a prime number

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

#### LCM (30, 17) = 2 × 3 × 5 × 17 = 510

### Calculate the expanding number of each fraction

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

#### For fraction: - ^{49}/_{30} is 510 ÷ 30 = (2 × 3 × 5 × 17) ÷ (2 × 3 × 5) = 17

#### For fraction: - ^{27}/_{17} is 510 ÷ 17 = (2 × 3 × 5 × 17) ÷ 17 = 30

### Expand the fractions

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

Multiply the numerators and denominators by their expanding number:

#### - ^{49}/_{30} = - ^{(17 × 49)}/_{(17 × 30)} = - ^{833}/_{510}

#### - ^{27}/_{17} = - ^{(30 × 27)}/_{(30 × 17)} = - ^{810}/_{510}

### The fractions have the same denominator, compare their numerators.

#### The larger the numerator the smaller the negative fraction.

## ::: Comparing operation :::

The final answer: