## The executed operation (with ordinary fractions):

^{21}/_{26} × - ^{14}/_{62}

### Rewrite the equivalent simplified operation:

#### Combine the signs of the fractions into a single one, placed in front of the expression.

^{21}/_{26} × - ^{14}/_{62} =

#### - ^{21}/_{26} × ^{14}/_{62}

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

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

#### Fraction: ^{21}/_{26} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

21 = 3 × 7;

26 = 2 × 13;

#### Fraction: ^{14}/_{62} =

^{(2 × 7)}/_{(2 × 31)} =

^{((2 × 7) ÷ 2)}/_{((2 × 31) ÷ 2)} =

^{(2 ÷ 2 × 7)}/_{(2 ÷ 2 × 31)} =

^{(1 × 7)}/_{(1 × 31)} =

^{7}/_{31};

### Rewrite the equivalent simplified operation:

#### - ^{21}/_{26} × ^{14}/_{62} =

#### - ^{21}/_{26} × ^{7}/_{31}

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

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

#### - ^{21}/_{26} × ^{7}/_{31} =

#### - ^{(21 × 7)} / _{(26 × 31)} =

#### - ^{(3 × 7 × 7)} / _{(2 × 13 × 31)} =

#### - ^{(3 × 72)} / _{(2 × 13 × 31)}

## Reduce (simplify) 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 the denominator have no common factors

#### gcf(3 × 7^{2}; 2 × 13 × 31) = 1

### Divide the numerator and the denominator by GCF.

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

#### - ^{(3 × 72)} / _{(2 × 13 × 31)} =

#### - ^{147}/_{806}

## Rewrite the fraction

### As a decimal number:

#### - ^{147}/_{806} =

#### - 147 ÷ 806 ≈

#### - 0.182382133995 ≈

#### - 0.18

### As a percentage:

#### - 0.182382133995 =

#### - 0.182382133995 × ^{100}/_{100} =

^{( - 0.182382133995 × 100)}/_{100} =

^{ - 18.238213399504}/_{100} ≈

#### - 18.238213399504% ≈

#### - 18.24%

## The final answer:

:: written in three ways ::