# Multiplying the common ordinary fractions: - ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} = ? The multiplication process explained. The result written: As a negative improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage

## - ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} = ?

## Simplify the operation

### 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 + then it is usually not written.

#### The sign of a multiplication operation:

#### + 1 × + 1 = + 1

#### + 1 × - 1 = - 1

#### - 1 × - 1 = + 1

#### - ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} =

#### - ^{27}/_{38} × ^{68}/_{14} × ^{9,098}/_{16} × ^{9,041}/_{25} × ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21}

## Simplify the operation

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

#### To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.

#### * By reducing the values of the numerators and the denominators of the fractions the calculations are easier to make.

#### A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

#### * In order to easily reduce a fraction, factor its numerator and denominator. This way all the common prime factors are easily identified and crossed out, without calculating the GCF.

^{27}/_{38} is already reduced to the lowest terms.

#### The numerator and denominator have no common prime factors.

#### Their prime factorization:

27 = 3^{3}

38 = 2 × 19

^{68}/_{14} =

^{(22 × 17)}/_{(2 × 7)} =

^{((22 × 17) ÷ 2)}/_{((2 × 7) ÷ 2)} =

^{(22 ÷ 2 × 17)}/_{(2 ÷ 2 × 7)} =

^{(2(2 - 1) × 17)}/_{(1 × 7)} =

^{(21 × 17)}/_{(1 × 7)} =

^{(2 × 17)}/_{(1 × 7)} =

^{34}/_{7}

^{9,098}/_{16} =

^{(2 × 4,549)}/_{24} =

^{((2 × 4,549) ÷ 2)}/_{(24 ÷ 2)} =

^{(2 ÷ 2 × 4,549)}/_{(24 ÷ 2)} =

^{(1 × 4,549)}/_{2(4 - 1)} =

^{(1 × 4,549)}/_{23} =

^{4,549}/_{8}

^{9,041}/_{25} is already reduced to the lowest terms.

#### The numerator and denominator have no common prime factors.

#### Their prime factorization:

9,041 is a prime number (it cannot be factored into other prime factors)

25 = 5^{2}

^{67}/_{16} is already reduced to the lowest terms.

#### The numerator and denominator have no common prime factors.

#### Their prime factorization:

67 is a prime number (it cannot be factored into other prime factors)

16 = 2^{4}

^{68}/_{20} =

^{(22 × 17)}/_{(22 × 5)} =

^{((22 × 17) ÷ 22)}/_{((22 × 5) ÷ 22)} =

^{(22 ÷ 22 × 17)}/_{(22 ÷ 22 × 5)} =

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

^{(20 × 17)}/_{(20 × 5)} =

^{(1 × 17)}/_{(1 × 5)} =

^{17}/_{5}

^{65}/_{15} =

^{(5 × 13)}/_{(3 × 5)} =

^{((5 × 13) ÷ 5)}/_{((3 × 5) ÷ 5)} =

^{(5 ÷ 5 × 13)}/_{(3 × 5 ÷ 5)} =

^{(1 × 13)}/_{(3 × 1)} =

^{13}/_{3}

^{50}/_{21} is already reduced to the lowest terms.

#### The numerator and denominator have no common prime factors.

#### Their prime factorization:

50 = 2 × 5^{2}

21 = 3 × 7

### Rewrite the equivalent simplified operation:

#### - ^{27}/_{38} × ^{68}/_{14} × ^{9,098}/_{16} × ^{9,041}/_{25} × ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} =

#### - ^{27}/_{38} × ^{34}/_{7} × ^{4,549}/_{8} × ^{9,041}/_{25} × ^{67}/_{16} × ^{17}/_{5} × ^{13}/_{3} × ^{50}/_{21}

## Perform the operation of calculating the fractions

### Multiply the fractions:

#### 1) Multiply the numerators, that is, all the numbers above the fractions bars, separately.

#### 2) Multiply the denominators, that is, all the numbers below the fractions bars, separately.

#### * Factor all the numerators and all the denominators in order to easily reduce (simplify) the end fraction.

#### - ^{27}/_{38} × ^{34}/_{7} × ^{4,549}/_{8} × ^{9,041}/_{25} × ^{67}/_{16} × ^{17}/_{5} × ^{13}/_{3} × ^{50}/_{21} =

#### - ^{(27 × 34 × 4,549 × 9,041 × 67 × 17 × 13 × 50)} / _{(38 × 7 × 8 × 25 × 16 × 5 × 3 × 21)} =

#### - ^{(33 × 2 × 17 × 4,549 × 9,041 × 67 × 17 × 13 × 2 × 52)} / _{(2 × 19 × 7 × 23 × 52 × 24 × 5 × 3 × 3 × 7)} =

#### - ^{(22 × 33 × 52 × 13 × 172 × 67 × 4,549 × 9,041)} / _{(28 × 32 × 53 × 72 × 19)}

## Fully reduce (simplify) the end fraction to its lowest terms equivalent:

### Calculate the greatest common factor, GCF,

of the numerator and denominator of the fraction:

#### A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

#### To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.

#### * To calculate the GCF, we need to factor the numerator and the denominator of the fraction into prime factors.

#### Then multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).

#### GCF (2^{2} × 3^{3} × 5^{2} × 13 × 17^{2} × 67 × 4,549 × 9,041; 2^{8} × 3^{2} × 5^{3} × 7^{2} × 19) = 2^{2} × 3^{2} × 5^{2}

### Divide the numerator and the denominator by their GCF:

#### - ^{(22 × 33 × 52 × 13 × 172 × 67 × 4,549 × 9,041)} / _{(28 × 32 × 53 × 72 × 19)} =

#### - ^{((22 × 33 × 52 × 13 × 172 × 67 × 4,549 × 9,041) ÷ (22 × 32 × 52))} / _{((28 × 32 × 53 × 72 × 19) ÷ (22 × 32 × 52))} =

#### - ^{(22 ÷ 22 × 33 ÷ 32 × 52 ÷ 52 × 13 × 172 × 67 × 4,549 × 9,041)}/_{(28 ÷ 22 × 32 ÷ 32 × 53 ÷ 52 × 72 × 19)} =

#### - ^{(2(2 - 2) × 3(3 - 2) × 5(2 - 2) × 13 × 172 × 67 × 4,549 × 9,041)}/_{(2(8 - 2) × 3(2 - 2) × 5(3 - 2) × 72 × 19)} =

#### - ^{(20 × 31 × 50 × 13 × 172 × 67 × 4,549 × 9,041)}/_{(26 × 30 × 51 × 72 × 19)} =

#### - ^{(1 × 3 × 1 × 13 × 172 × 67 × 4,549 × 9,041)}/_{(26 × 1 × 5 × 72 × 19)} =

#### - ^{(3 × 13 × 172 × 67 × 4,549 × 9,041)}/_{(26 × 5 × 72 × 19)} =

#### - ^{(3 × 13 × 289 × 67 × 4,549 × 9,041)}/_{(64 × 5 × 49 × 19)} =

#### - ^{31,057,726,313,913}/_{297,920}

## Rewrite the fraction

### As a mixed number (also called a mixed fraction):

#### A mixed number: a whole number and a proper fraction, both having the same sign.

#### A proper fraction: the value of the numerator is smaller than the value of the denominator.

#### Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:

#### - 31,057,726,313,913 ÷ 297,920 = - 104,248,544 and the remainder = - 85,433 ⇒

#### - 31,057,726,313,913 = - 104,248,544 × 297,920 - 85,433 ⇒

#### - ^{31,057,726,313,913}/_{297,920} =

^{( - 104,248,544 × 297,920 - 85,433)}/_{297,920} =

^{( - 104,248,544 × 297,920)}/_{297,920} - ^{85,433}/_{297,920} =

#### - 104,248,544 - ^{85,433}/_{297,920} =

#### - 104,248,544 ^{85,433}/_{297,920}

### As a decimal number:

#### Simply divide the numerator by the denominator, without a remainder, as shown below:

#### - 104,248,544 - ^{85,433}/_{297,920} =

#### - 104,248,544 - 85,433 ÷ 297,920 ≈

#### - 104,248,544.28676490333 ≈

#### - 104,248,544.29

### As a percentage:

#### A percentage value p% is equal to the fraction: ^{p}/_{100}, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.

#### To do that, multiply the number by the fraction ^{100}/_{100}.

#### The value of the fraction ^{100}/_{100} = 1, so by multiplying the number by this fraction the result is not changing, only the form.

#### - 104,248,544.28676490333 =

#### - 104,248,544.28676490333 × ^{100}/_{100} =

^{( - 104,248,544.28676490333 × 100)}/_{100} =

^{ - 10,424,854,428.676490332975}/_{100} ≈

#### - 10,424,854,428.676490332975% ≈

#### - 10,424,854,428.68%

## The final answer:

written in four ways

## As a negative improper fraction:

(the numerator >= the denominator)

- ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} = - ^{31,057,726,313,913}/_{297,920}

## As a mixed number (also called a mixed fraction):

- ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} = - 104,248,544 ^{85,433}/_{297,920}

## As a decimal number:

- ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} ≈ - 104,248,544.29

## As a percentage:

- ^{27}/_{38} × - ^{68}/_{14} × - ^{9,098}/_{16} × - ^{9,041}/_{25} × - ^{67}/_{16} × ^{68}/_{20} × ^{65}/_{15} × ^{50}/_{21} ≈ - 10,424,854,428.68%

#### How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

## Other similar operations

## Multiply common ordinary fractions, online calculator: