## Reduce: ^{6,609}/_{27}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{6,609}/_{27}

#### The number above the bar is the numerator: 6,609

#### The number below the bar is the denominator: 27

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

^{6,609}/_{27} = 6,609 ÷ 27

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

Value = 6,609 ÷ 27

### 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.

#### 6,609 = 3 × 2,203;

6,609 is not a prime, is a composite number;

#### 27 = 3^{3};

27 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 (6,609; 27) = 3

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

^{6,609}/_{27} =

^{(3 × 2,203)}/_{33} =

^{((3 × 2,203) ÷ 3)} / _{(33 ÷ 3)} =

^{2,203}/_{32} =

^{2,203}/_{9}

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

^{2,203}/_{9} 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.

#### 2,203 ÷ 9 = 244 and remainder = 7 =>

#### 2,203 = 244 × 9 + 7 =>

^{2,203}/_{9} =

^{(244 × 9 + 7)} / _{9} =

^{(244 × 9)} / _{9} + ^{7} / _{9} =

#### 244 + ^{7}/_{9} =

#### 244 ^{7}/_{9}

### As a decimal number:

#### 244 ^{7}/_{9} =

#### 244 + ^{7}/_{9} =

#### 244 + 7 ÷ 9 ≈

#### 244.777777777778 ≈

#### 244.78

### As a percentage:

#### 244.777777777778 =

#### 244.777777777778 × ^{100}/_{100} =

#### ^{24,477.777777777778}/_{100} =

#### 24,477.777777777778% ≈

#### 24,477.78%

#### 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):

^{6,609}/_{27} = ^{2,203}/_{9}

## As a mixed number (mixed fraction)

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

^{6,609}/_{27} = 244 ^{7}/_{9}

## As a decimal number:

^{6,609}/_{27} ≈ 244.777777777778 ≈ 244.78

## As a percentage:

^{6,609}/_{27} ≈ 24,477.78%

## More operations of this kind:

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