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

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

#### Fraction: ^{588}/_{44} =

^{(22 × 3 × 72)}/_{(22 × 11)} =

^{((22 × 3 × 72) ÷ 22)}/_{((22 × 11) ÷ 22)} =

^{(22 ÷ 22 × 3 × 72)}/_{(22 ÷ 22 × 11)} =

^{(2(2 - 2) × 3 × 72)}/_{(2(2 - 2) × 11)} =

^{(20 × 3 × 72)}/_{(20 × 11)} =

^{(1 × 3 × 72)}/_{(1 × 11)} =

^{147}/_{11};

#### Fraction: ^{80}/_{50} =

^{(24 × 5)}/_{(2 × 52)} =

^{((24 × 5) ÷ (2 × 5))}/_{((2 × 52) ÷ (2 × 5))} =

^{(24 ÷ 2 × 5 ÷ 5)}/_{(2 ÷ 2 × 52 ÷ 5)} =

^{(2(4 - 1) × 1)}/_{(1 × 5(2 - 1))} =

^{(23 × 1)}/_{(1 × 51)} =

^{(23 × 1)}/_{(1 × 5)} =

^{8}/_{5};

### Rewrite the equivalent simplified operation:

#### - ^{588}/_{44} × ^{80}/_{50} =

#### - ^{147}/_{11} × ^{8}/_{5}

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

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

#### - ^{147}/_{11} × ^{8}/_{5} =

#### - ^{(147 × 8)} / _{(11 × 5)} =

#### - ^{(3 × 72 × 23)} / _{(11 × 5)} =

#### - ^{(23 × 3 × 72)} / _{(5 × 11)}

## 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(2^{3} × 3 × 7^{2}; 5 × 11) = 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.

#### - ^{(23 × 3 × 72)} / _{(5 × 11)} =

#### - ^{1,176}/_{55}

## 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.

#### - 1,176 ÷ 55 = - 21 and remainder = - 21 =>

#### - 1,176 = - 21 × 55 - 21 =>

#### - ^{1,176}/_{55} =

^{( - 21 × 55 - 21)}/_{55} =

^{( - 21 × 55)}/_{55} - ^{21}/_{55} =

#### - 21 - ^{21}/_{55} =

#### - 21 ^{21}/_{55}

### As a decimal number:

#### - 21 - ^{21}/_{55} =

#### - 21 - 21 ÷ 55 ≈

#### - 21.381818181818 ≈

#### - 21.38

### As a percentage:

#### - 21.381818181818 =

#### - 21.381818181818 × ^{100}/_{100} =

^{( - 21.381818181818 × 100)}/_{100} =

^{ - 2,138.181818181818}/_{100} ≈

#### - 2,138.181818181818% ≈

#### - 2,138.18%

## The final answer:

:: written in four ways ::