## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{82,388}/_{60}

#### The number above the bar is the numerator: 82,388

#### The number below the bar is the denominator: 60

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

^{82,388}/_{60} = 82,388 ÷ 60

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

Value = 82,388 ÷ 60

### 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.

#### 82,388 = 2^{2} × 43 × 479;

82,388 is not a prime, is a composite number;

#### 60 = 2^{2} × 3 × 5;

60 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 (82,388; 60) = 2^{2} = 4

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

^{82,388}/_{60} =

^{(22 × 43 × 479)}/_{(22 × 3 × 5)} =

^{((22 × 43 × 479) ÷ 22)} / _{((22 × 3 × 5) ÷ 22)} =

^{(43 × 479)}/_{(3 × 5)} =

^{20,597}/_{15}

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

^{20,597}/_{15} 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.

#### 20,597 ÷ 15 = 1,373 and remainder = 2 =>

#### 20,597 = 1,373 × 15 + 2 =>

^{20,597}/_{15} =

^{(1,373 × 15 + 2)} / _{15} =

^{(1,373 × 15)} / _{15} + ^{2} / _{15} =

#### 1,373 + ^{2}/_{15} =

#### 1,373 ^{2}/_{15}

### As a decimal number:

#### 1,373 ^{2}/_{15} =

#### 1,373 + ^{2}/_{15} =

#### 1,373 + 2 ÷ 15 ≈

#### 1,373.133333333333 ≈

#### 1,373.13

### As a percentage:

#### 1,373.133333333333 =

#### 1,373.133333333333 × ^{100}/_{100} =

#### ^{137,313.333333333333}/_{100} =

#### 137,313.333333333333% ≈

#### 137,313.33%

#### 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...