## Reduce: ^{6,332}/_{48}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{6,332}/_{48}

#### The number above the bar is the numerator: 6,332

#### The number below the bar is the denominator: 48

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

^{6,332}/_{48} = 6,332 ÷ 48

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

Value = 6,332 ÷ 48

### 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.

#### 6,332 = 2^{2} × 1,583;

6,332 is not a prime, is a composite number;

#### 48 = 2^{4} × 3;

48 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 (6,332; 48) = 2^{2} = 4

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

^{6,332}/_{48} =

^{(22 × 1,583)}/_{(24 × 3)} =

^{((22 × 1,583) ÷ 22)} / _{((24 × 3) ÷ 22)} =

^{1,583}/_{(22 × 3)} =

^{1,583}/_{12}

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

^{1,583}/_{12} 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.

#### 1,583 ÷ 12 = 131 and remainder = 11 =>

#### 1,583 = 131 × 12 + 11 =>

^{1,583}/_{12} =

^{(131 × 12 + 11)} / _{12} =

^{(131 × 12)} / _{12} + ^{11} / _{12} =

#### 131 + ^{11}/_{12} =

#### 131 ^{11}/_{12}

### As a decimal number:

#### 131 ^{11}/_{12} =

#### 131 + ^{11}/_{12} =

#### 131 + 11 ÷ 12 ≈

#### 131.916666666667 ≈

#### 131.92

### As a percentage:

#### 131.916666666667 =

#### 131.916666666667 × ^{100}/_{100} =

#### ^{13,191.666666666667}/_{100} =

#### 13,191.666666666667% ≈

#### 13,191.67%

#### 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):

^{6,332}/_{48} = ^{1,583}/_{12}

## As a mixed number (mixed fraction)

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

^{6,332}/_{48} = 131 ^{11}/_{12}

## As a decimal number:

^{6,332}/_{48} ≈ 131.916666666667 ≈ 131.92

## As a percentage:

^{6,332}/_{48} ≈ 13,191.67%

## More operations of this kind:

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