### Rewrite the equivalent simplified operation:

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

#### The sign of the multiplication: + 1 × + 1 = + 1; + 1 × - 1 = - 1; - 1 × - 1 = + 1.

^{11}/_{34} × ^{30}/_{12} × - ^{44}/_{16} =

#### - ^{11}/_{34} × ^{30}/_{12} × ^{44}/_{16}

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

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

#### Fraction: ^{11}/_{34} already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

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

34 = 2 × 17;

#### Fraction: ^{30}/_{12} =

^{(2 × 3 × 5)}/_{(22 × 3)} =

^{((2 × 3 × 5) ÷ (2 × 3))}/_{((22 × 3) ÷ (2 × 3))} =

^{(2 ÷ 2 × 3 ÷ 3 × 5)}/_{(22 ÷ 2 × 3 ÷ 3)} =

^{(1 × 1 × 5)}/_{(2(2 - 1) × 1)} =

^{(1 × 1 × 5)}/_{(2 × 1)} =

^{5}/_{2};

#### Fraction: ^{44}/_{16} =

^{(22 × 11)}/_{24} =

^{((22 × 11) ÷ 22)}/_{(24 ÷ 22)} =

^{(22 ÷ 22 × 11)}/_{(24 ÷ 22)} =

^{(2(2 - 2) × 11)}/_{2(4 - 2)} =

^{(20 × 11)}/_{22} =

^{(1 × 11)}/_{22} =

^{11}/_{4};

### Rewrite the equivalent simplified operation:

#### - ^{11}/_{34} × ^{30}/_{12} × ^{44}/_{16} =

#### - ^{11}/_{34} × ^{5}/_{2} × ^{11}/_{4}

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

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

#### - ^{11}/_{34} × ^{5}/_{2} × ^{11}/_{4} =

#### - ^{(11 × 5 × 11)} / _{(34 × 2 × 4)} =

#### - ^{(11 × 5 × 11)} / _{(2 × 17 × 2 × 22)} =

#### - ^{(5 × 112)} / _{(24 × 17)}

## 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(5 × 11^{2}; 2^{4} × 17) = 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.

#### - ^{(5 × 112)} / _{(24 × 17)} =

#### - ^{605}/_{272}

## 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.

#### - 605 ÷ 272 = - 2 and remainder = - 61 =>

#### - 605 = - 2 × 272 - 61 =>

#### - ^{605}/_{272} =

^{( - 2 × 272 - 61)}/_{272} =

^{( - 2 × 272)}/_{272} - ^{61}/_{272} =

#### - 2 - ^{61}/_{272} =

#### - 2 ^{61}/_{272}