## The executed operation (with ordinary fractions):

^{539}/_{35} × ^{80}/_{27} × ^{6,725}/_{26} × ^{9,985}/_{35} × - ^{81}/_{33} × - ^{76}/_{38} × ^{74}/_{29} × - ^{10,040}/_{29}

### Rewrite the equivalent simplified operation:

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

^{539}/_{35} × ^{80}/_{27} × ^{6,725}/_{26} × ^{9,985}/_{35} × - ^{81}/_{33} × - ^{76}/_{38} × ^{74}/_{29} × - ^{10,040}/_{29} =

#### - ^{539}/_{35} × ^{80}/_{27} × ^{6,725}/_{26} × ^{9,985}/_{35} × ^{81}/_{33} × ^{76}/_{38} × ^{74}/_{29} × ^{10,040}/_{29}

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

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

#### Fraction: ^{539}/_{35} =

^{(72 × 11)}/_{(5 × 7)} =

^{((72 × 11) ÷ 7)}/_{((5 × 7) ÷ 7)} =

^{(72 ÷ 7 × 11)}/_{(5 × 7 ÷ 7)} =

^{(7(2 - 1) × 11)}/_{(5 × 1)} =

^{(71 × 11)}/_{(5 × 1)} =

^{(7 × 11)}/_{(5 × 1)} =

^{77}/_{5};

#### Fraction: ^{80}/_{27} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

80 = 2^{4} × 5;

27 = 3^{3};

#### Fraction: ^{6,725}/_{26} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

6,725 = 5^{2} × 269;

26 = 2 × 13;

#### Fraction: ^{9,985}/_{35} =

^{(5 × 1,997)}/_{(5 × 7)} =

^{((5 × 1,997) ÷ 5)}/_{((5 × 7) ÷ 5)} =

^{(5 ÷ 5 × 1,997)}/_{(5 ÷ 5 × 7)} =

^{(1 × 1,997)}/_{(1 × 7)} =

^{1,997}/_{7};

#### Fraction: ^{81}/_{33} =

^{34}/_{(3 × 11)} =

^{(34 ÷ 3)}/_{((3 × 11) ÷ 3)} =

^{(34 ÷ 3)}/_{(3 ÷ 3 × 11)} =

^{3(4 - 1)}/_{(1 × 11)} =

^{33}/_{(1 × 11)} =

^{27}/_{11};

#### Fraction: ^{76}/_{38} =

^{(22 × 19)}/_{(2 × 19)} =

^{((22 × 19) ÷ (2 × 19))}/_{((2 × 19) ÷ (2 × 19))} =

^{(22 ÷ 2 × 19 ÷ 19)}/_{(2 ÷ 2 × 19 ÷ 19)} =

^{(2(2 - 1) × 1)}/_{(1 × 1)} =

^{(2 × 1)}/_{(1 × 1)} =

^{2}/_{1} =

#### 2;

#### Fraction: ^{74}/_{29} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

74 = 2 × 37;

29 is a prime number;

#### Fraction: ^{10,040}/_{29} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

10,040 = 2^{3} × 5 × 251;

29 is a prime number;

### Rewrite the equivalent simplified operation:

#### - ^{539}/_{35} × ^{80}/_{27} × ^{6,725}/_{26} × ^{9,985}/_{35} × ^{81}/_{33} × ^{76}/_{38} × ^{74}/_{29} × ^{10,040}/_{29} =

#### - ^{77}/_{5} × ^{80}/_{27} × ^{6,725}/_{26} × ^{1,997}/_{7} × ^{27}/_{11} × 2 × ^{74}/_{29} × ^{10,040}/_{29}

### These fractions reduce each other, there are numerators and denominators of equal values:

#### Fractions: ^{80}/_{27} × ^{27}/_{11} = ^{80}/_{11}

### Rewrite the equivalent simplified operation:

#### - ^{77}/_{5} × ^{80}/_{27} × ^{6,725}/_{26} × ^{1,997}/_{7} × ^{27}/_{11} × 2 × ^{74}/_{29} × ^{10,040}/_{29} =

#### - ^{77}/_{5} × ^{80}/_{11} × ^{6,725}/_{26} × ^{1,997}/_{7} × 2 × ^{74}/_{29} × ^{10,040}/_{29}

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

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

#### Fraction: ^{80}/_{11} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

80 = 2^{4} × 5;

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.

#### - ^{77}/_{5} × ^{80}/_{11} × ^{6,725}/_{26} × ^{1,997}/_{7} × 2 × ^{74}/_{29} × ^{10,040}/_{29} =

#### - ^{(77 × 80 × 6,725 × 1,997 × 2 × 74 × 10,040)} / _{(5 × 11 × 26 × 7 × 29 × 29)} =

#### - ^{(7 × 11 × 24 × 5 × 52 × 269 × 1,997 × 2 × 2 × 37 × 23 × 5 × 251)} / _{(5 × 11 × 2 × 13 × 7 × 29 × 29)} =

#### - ^{(29 × 54 × 7 × 11 × 37 × 251 × 269 × 1,997)} / _{(2 × 5 × 7 × 11 × 13 × 292)}

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

### Calculate the greatest common factor, GCF:

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

#### gcf(2^{9} × 5^{4} × 7 × 11 × 37 × 251 × 269 × 1,997; 2 × 5 × 7 × 11 × 13 × 29^{2}) = 2 × 5 × 7 × 11

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

#### - ^{(29 × 54 × 7 × 11 × 37 × 251 × 269 × 1,997)} / _{(2 × 5 × 7 × 11 × 13 × 292)} =

#### - ^{((29 × 54 × 7 × 11 × 37 × 251 × 269 × 1,997) ÷ (2 × 5 × 7 × 11))} / _{((2 × 5 × 7 × 11 × 13 × 292) ÷ (2 × 5 × 7 × 11))} =

#### - ^{(29 ÷ 2 × 54 ÷ 5 × 7 ÷ 7 × 11 ÷ 11 × 37 × 251 × 269 × 1,997)}/_{(2 ÷ 2 × 5 ÷ 5 × 7 ÷ 7 × 11 ÷ 11 × 13 × 292)} =

#### - ^{(2(9 - 1) × 5(4 - 1) × 1 × 1 × 37 × 251 × 269 × 1,997)}/_{(1 × 1 × 1 × 1 × 13 × 292)} =

#### - ^{(28 × 53 × 1 × 1 × 37 × 251 × 269 × 1,997)}/_{(1 × 1 × 1 × 1 × 13 × 292)} =

#### - ^{(28 × 53 × 37 × 251 × 269 × 1,997)}/_{(13 × 292)} =

#### - ^{(256 × 125 × 37 × 251 × 269 × 1,997)}/_{(13 × 841)} =

#### - ^{159,645,164,512,000}/_{10,933};

## 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.

#### - 159,645,164,512,000 ÷ 10,933 = - 14,602,137,063 and remainder = - 2,221 =>

#### - 159,645,164,512,000 = - 14,602,137,063 × 10,933 - 2,221 =>

#### - ^{159,645,164,512,000}/_{10,933} =

^{( - 14,602,137,063 × 10,933 - 2,221)}/_{10,933} =

^{( - 14,602,137,063 × 10,933)}/_{10,933} - ^{2,221}/_{10,933} =

#### - 14,602,137,063 - ^{2,221}/_{10,933} =

#### - 14,602,137,063 ^{2,221}/_{10,933}

### As a decimal number:

#### - 14,602,137,063 - ^{2,221}/_{10,933} =

#### - 14,602,137,063 - 2,221 ÷ 10,933 ≈

#### - 14,602,137,063.203146437391 ≈

#### - 14,602,137,063.2

### As a percentage:

#### - 14,602,137,063.203146437391 =

#### - 14,602,137,063.203146437391 × ^{100}/_{100} =

^{( - 14,602,137,063.203146437391 × 100)}/_{100} =

^{ - 1,460,213,706,320.314643739138}/_{100} ≈

#### - 1,460,213,706,320.314643739138% ≈

#### - 1,460,213,706,320.31%

## The final answer:

:: written in four ways ::