## Reduce: ^{56,214}/_{100}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{56,214}/_{100}

#### The number above the bar is the numerator: 56,214

#### The number below the bar is the denominator: 100

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

^{56,214}/_{100} = 56,214 ÷ 100

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

Value = 56,214 ÷ 100

### 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.

#### 56,214 = 2 × 3^{4} × 347;

56,214 is not a prime, is a composite number;

#### 100 = 2^{2} × 5^{2};

100 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 (56,214; 100) = 2

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

^{56,214}/_{100} =

^{(2 × 34 × 347)}/_{(22 × 52)} =

^{((2 × 34 × 347) ÷ 2)} / _{((22 × 52) ÷ 2)} =

^{(34 × 347)}/_{(2 × 52)} =

^{28,107}/_{50}

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

^{28,107}/_{50} 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.

#### 28,107 ÷ 50 = 562 and remainder = 7 =>

#### 28,107 = 562 × 50 + 7 =>

^{28,107}/_{50} =

^{(562 × 50 + 7)} / _{50} =

^{(562 × 50)} / _{50} + ^{7} / _{50} =

#### 562 + ^{7}/_{50} =

#### 562 ^{7}/_{50}

### As a decimal number:

#### 562 ^{7}/_{50} =

#### 562 + ^{7}/_{50} =

#### 562 + 7 ÷ 50 =

#### 562.14

### As a percentage:

#### 562.14 =

#### 562.14 × ^{100}/_{100} =

#### ^{56,214}/_{100} =

#### 56,214%

#### 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):

^{56,214}/_{100} = ^{28,107}/_{50}

## As a mixed number (mixed fraction)

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

^{56,214}/_{100} = 562 ^{7}/_{50}

## As a decimal number:

^{56,214}/_{100} = 562.14

## As a percentage:

^{56,214}/_{100} = 56,214%

## More operations of this kind:

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