## Reduce: ^{6,609}/_{3,969}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{6,609}/_{3,969}

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

#### The number below the bar is the denominator: 3,969

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

^{6,609}/_{3,969} = 6,609 ÷ 3,969

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

Value = 6,609 ÷ 3,969

### 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;

#### 3,969 = 3^{4} × 7^{2};

3,969 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; 3,969) = 3

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

^{6,609}/_{3,969} =

^{(3 × 2,203)}/_{(34 × 72)} =

^{((3 × 2,203) ÷ 3)} / _{((34 × 72) ÷ 3)} =

^{2,203}/_{(33 × 72)} =

^{2,203}/_{1,323}

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

^{2,203}/_{1,323} 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 ÷ 1,323 = 1 and remainder = 880 =>

#### 2,203 = 1 × 1,323 + 880 =>

^{2,203}/_{1,323} =

^{(1 × 1,323 + 880)} / _{1,323} =

^{(1 × 1,323)} / _{1,323} + ^{880} / _{1,323} =

#### 1 + ^{880}/_{1,323} =

#### 1 ^{880}/_{1,323}

### As a decimal number:

#### 1 ^{880}/_{1,323} =

#### 1 + ^{880}/_{1,323} =

#### 1 + 880 ÷ 1,323 ≈

#### 1.665154950869 ≈

#### 1.67

### As a percentage:

#### 1.665154950869 =

#### 1.665154950869 × ^{100}/_{100} =

#### ^{166.515495086924}/_{100} =

#### 166.515495086924% ≈

#### 166.52%

#### 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}/_{3,969} = ^{2,203}/_{1,323}

## As a mixed number (mixed fraction)

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

^{6,609}/_{3,969} = 1 ^{880}/_{1,323}

## As a decimal number:

^{6,609}/_{3,969} ≈ 1.665154950869 ≈ 1.67

## As a percentage:

^{6,609}/_{3,969} ≈ 166.52%

## More operations of this kind:

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