## Reduce: ^{11,880,006}/_{9,504,011}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{11,880,006}/_{9,504,011}

#### The number above the bar is the numerator: 11,880,006

#### The number below the bar is the denominator: 9,504,011

#### The fraction bar means that the two numbers are dividing themselves:

^{11,880,006}/_{9,504,011} = 11,880,006 ÷ 9,504,011

#### Divide the numerator by the denominator to get fraction's value:

Value = 11,880,006 ÷ 9,504,011

### Introduction. Percent

#### 'Percent (%)' means 'out of one hundred':

#### p% = p 'out of one hundred',

#### p% = ^{p}/_{100} = p ÷ 100

### Note:

#### The fraction ^{100}/_{100} = 100 ÷ 100 = 100% = 1

#### Multiply a number by the fraction ^{100}/_{100},

... and its value doesn't change.

## To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

#### To calculate the greatest common factor, we build the prime factorization of the two numbers.

### Integer numbers prime factorization:

#### Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

#### 11,880,006 = 2 × 3 × 23 × 31 × 2,777;

11,880,006 is not a prime, is a composite number;

#### 9,504,011 = 11 × 31 × 47 × 593;

9,504,011 is not a prime, is a composite number;

** Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself. *

* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

### Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

#### Multiply all the common prime factors, by the lowest exponents (if any).

#### gcf, hcf, gcd (11,880,006; 9,504,011) = 31

### Divide both the numerator and the denominator by their greatest common factor.

^{11,880,006}/_{9,504,011} =

^{(2 × 3 × 23 × 31 × 2,777)}/_{(11 × 31 × 47 × 593)} =

^{((2 × 3 × 23 × 31 × 2,777) ÷ 31)} / _{((11 × 31 × 47 × 593) ÷ 31)} =

^{(2 × 3 × 23 × 2,777)}/_{(11 × 47 × 593)} =

^{383,226}/_{306,581}

## The fraction is now reduced to the lowest terms.

^{383,226}/_{306,581} is an improper fraction.

#### An improper fraction: numerator larger than denominator.

## Rewrite the end result, continued below...

## Rewrite the fraction:

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

#### A mixed number (mixed fraction): a whole number and a proper fraction, of the same sign.

#### A proper fraction: numerator smaller than denominator.

#### 383,226 ÷ 306,581 = 1 and remainder = 76,645 =>

#### 383,226 = 1 × 306,581 + 76,645 =>

^{383,226}/_{306,581} =

^{(1 × 306,581 + 76645)} / _{306,581} =

^{(1 × 306,581)} / _{306,581} + ^{76645} / _{306,581} =

#### 1 + ^{76,645}/_{306,581} =

#### 1 ^{76,645}/_{306,581}

### As a decimal number:

#### 1 ^{76,645}/_{306,581} =

#### 1 + ^{76,645}/_{306,581} =

#### 1 + 76,645 ÷ 306,581 ≈

#### 1.249999184555 ≈

#### 1.25

### As a percentage:

#### 1.249999184555 =

#### 1.249999184555 × ^{100}/_{100} =

#### ^{124.999918455482}/_{100} =

#### 124.999918455482% ≈

#### 125%

#### In other words:

#### 1) Calculate fraction's value.

#### 2) Multiply that number by 100.

#### 3) Add the percent sign % to it.

## Final answer

continued below...

## Final answer:

:: written in four ways ::

## As an improper fraction

(numerator larger than denominator):

^{11,880,006}/_{9,504,011} = ^{383,226}/_{306,581}

## As a mixed number (mixed fraction)

(a whole number and a proper fraction, of the same sign):

^{11,880,006}/_{9,504,011} = 1 ^{76,645}/_{306,581}

## As a decimal number:

^{11,880,006}/_{9,504,011} ≈ 1.249999184555 ≈ 1.25

## As a percentage:

^{11,880,006}/_{9,504,011} ≈ 125%

## More operations of this kind:

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