## The operation of comparing fractions:

^{- 922}/_{56} and ^{- 931}/_{59}

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

#### - ^{922}/_{56} = - ^{(2 × 461)}/_{(23 × 7)} = - ^{((2 × 461) ÷ 2)}/_{((23 × 7) ÷ 2)} = - ^{461}/_{28}

#### - ^{931}/_{59} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

931 = 7^{2} × 19;

59 is a prime number;

## 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:

#### 28 = 2^{2} × 7

#### 59 is a prime number

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

#### LCM (28, 59) = 2^{2} × 7 × 59 = 1,652

### Calculate the expanding number of each fraction

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

#### For fraction: - ^{461}/_{28} is 1,652 ÷ 28 = (2^{2} × 7 × 59) ÷ (2^{2} × 7) = 59

#### For fraction: - ^{931}/_{59} is 1,652 ÷ 59 = (2^{2} × 7 × 59) ÷ 59 = 28

### Expand the fractions

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

Multiply the numerators and denominators by their expanding number:

#### - ^{461}/_{28} = - ^{(59 × 461)}/_{(59 × 28)} = - ^{27,199}/_{1,652}

#### - ^{931}/_{59} = - ^{(28 × 931)}/_{(28 × 59)} = - ^{26,068}/_{1,652}

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

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

## ::: Comparing operation :::

The final answer: