## Reduce: ^{6,556}/_{9,360}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{6,556}/_{9,360}

#### The number above the bar is the numerator: 6,556

#### The number below the bar is the denominator: 9,360

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

^{6,556}/_{9,360} = 6,556 ÷ 9,360

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

Value = 6,556 ÷ 9,360

### 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.

#### 6,556 = 2^{2} × 11 × 149;

6,556 is not a prime, is a composite number;

#### 9,360 = 2^{4} × 3^{2} × 5 × 13;

9,360 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 (6,556; 9,360) = 2^{2} = 4

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

^{6,556}/_{9,360} =

^{(22 × 11 × 149)}/_{(24 × 32 × 5 × 13)} =

^{((22 × 11 × 149) ÷ 22)} / _{((24 × 32 × 5 × 13) ÷ 22)} =

^{(11 × 149)}/_{(22 × 32 × 5 × 13)} =

^{1,639}/_{2,340}

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

^{1,639}/_{2,340} is a proper fraction.

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

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

## Rewrite the end result:

### As a decimal number:

^{1,639}/_{2,340} =

#### 1,639 ÷ 2,340 ≈

#### 0.700427350427 ≈

#### 0.7

### As a percentage:

#### 0.700427350427 =

#### 0.700427350427 × ^{100}/_{100} =

#### ^{70.042735042735}/_{100} =

#### 70.042735042735% ≈

#### 70.04%

#### 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 three ways ::

## As a proper fraction

(numerator smaller than denominator):

^{6,556}/_{9,360} = ^{1,639}/_{2,340}

## As a decimal number:

^{6,556}/_{9,360} ≈ 0.700427350427 ≈ 0.7

## As a percentage:

^{6,556}/_{9,360} ≈ 70.04%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions