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

#### Factor all the numbers in order to easily reduce (simplify) the end fraction.

#### Fraction: ^{627}/_{17} already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

627 = 3 × 11 × 19;

17 is a prime number, it cannot be factored into other prime factors;

#### Fraction: ^{21}/_{31} already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

21 = 3 × 7;

31 is a prime number, it cannot be factored into other prime factors;

### Multiply the numerators and denominators of the fractions separately:

#### Factor all the numbers in order to easily reduce (simplify) the end fraction.

#### - ^{627}/_{17} × ^{21}/_{31} =

#### - ^{(627 × 21)} / _{(17 × 31)} =

#### - ^{(3 × 11 × 19 × 3 × 7)} / _{(17 × 31)} =

#### - ^{(32 × 7 × 11 × 19)} / _{(17 × 31)}

## Reduce (simplify) the fraction to its lowest terms equivalent:

### Calculate the greatest common factor, GCF:

#### Multiply all the common prime factors, by the lowest exponents.

#### But, the numerator and denominator have no common factors.

#### gcf(3^{2} × 7 × 11 × 19; 17 × 31) = 1

### Divide the numerator and denominator by GCF.

#### The numerator and denominator of the fraction are coprime numbers (no common prime factors, GCF = 1). The fraction cannot be reduced (simplified): irreducible fraction.

#### - ^{(32 × 7 × 11 × 19)} / _{(17 × 31)} =

#### - ^{13,167}/_{527}

## Rewrite the fraction

### As a mixed number (also called a mixed fraction):

#### Mixed number = a whole number and a proper fraction, of the same sign.

#### Proper fraction = numerator smaller than denominator.

#### - 13,167 ÷ 527 = - 24 and remainder = - 519 =>

#### - 13,167 = - 24 × 527 - 519 =>

#### - ^{13,167}/_{527} =

^{( - 24 × 527 - 519)}/_{527} =

^{( - 24 × 527)}/_{527} - ^{519}/_{527} =

#### - 24 - ^{519}/_{527} =

#### - 24 ^{519}/_{527}

### As a decimal number:

#### - 24 - ^{519}/_{527} =

#### - 24 - 519 ÷ 527 ≈

#### - 24.984819734345 ≈

#### - 24.98

### As a percentage:

#### - 24.984819734345 =

#### - 24.984819734345 × ^{100}/_{100} =

^{( - 24.984819734345 × 100)}/_{100} =

^{ - 2,498.481973434535}/_{100} ≈

#### - 2,498.481973434535% ≈

#### - 2,498.48%

## The final answer:

:: written in four ways ::