## The executed operation (with ordinary fractions):

- ^{551}/_{21} × - ^{94}/_{11}

### Rewrite the equivalent simplified operation:

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

If the sign is +, it is no longer written.

#### - ^{551}/_{21} × - ^{94}/_{11} =

^{551}/_{21} × ^{94}/_{11}

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

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

#### Fraction: ^{551}/_{21} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

551 = 19 × 29;

21 = 3 × 7;

#### Fraction: ^{94}/_{11} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

94 = 2 × 47;

11 is a prime number;

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

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

^{551}/_{21} × ^{94}/_{11} =

^{(551 × 94)} / _{(21 × 11)} =

^{(19 × 29 × 2 × 47)} / _{(3 × 7 × 11)} =

^{(2 × 19 × 29 × 47)} / _{(3 × 7 × 11)}

## 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(2 × 19 × 29 × 47; 3 × 7 × 11) = 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.

^{(2 × 19 × 29 × 47)} / _{(3 × 7 × 11)} =

^{51,794}/_{231}

## 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.

#### 51,794 ÷ 231 = 224 and remainder = 50 =>

#### 51,794 = 224 × 231 + 50 =>

^{51,794}/_{231} =

^{(224 × 231 + 50)}/_{231} =

^{(224 × 231)}/_{231} + ^{50}/_{231} =

#### 224 + ^{50}/_{231} =

#### 224 ^{50}/_{231}

### As a decimal number:

#### 224 + ^{50}/_{231} =

#### 224 + 50 ÷ 231 ≈

#### 224.21645021645 ≈

#### 224.22

### As a percentage:

#### 224.21645021645 =

#### 224.21645021645 × ^{100}/_{100} =

^{(224.21645021645 × 100)}/_{100} =

^{22,421.645021645022}/_{100} ≈

#### 22,421.645021645022% ≈

#### 22,421.65%

## The final answer:

:: written in four ways ::