## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{8,464}/_{102}

#### The number above the bar is the numerator: 8,464

#### The number below the bar is the denominator: 102

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

^{8,464}/_{102} = 8,464 ÷ 102

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

Value = 8,464 ÷ 102

### 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.

#### 8,464 = 2^{4} × 23^{2};

8,464 is not a prime, is a composite number;

#### 102 = 2 × 3 × 17;

102 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 (8,464; 102) = 2

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

^{8,464}/_{102} =

^{(24 × 232)}/_{(2 × 3 × 17)} =

^{((24 × 232) ÷ 2)} / _{((2 × 3 × 17) ÷ 2)} =

^{(23 × 232)}/_{(3 × 17)} =

^{4,232}/_{51}

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

^{4,232}/_{51} 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.

#### 4,232 ÷ 51 = 82 and remainder = 50 =>

#### 4,232 = 82 × 51 + 50 =>

^{4,232}/_{51} =

^{(82 × 51 + 50)} / _{51} =

^{(82 × 51)} / _{51} + ^{50} / _{51} =

#### 82 + ^{50}/_{51} =

#### 82 ^{50}/_{51}

### As a decimal number:

#### 82 ^{50}/_{51} =

#### 82 + ^{50}/_{51} =

#### 82 + 50 ÷ 51 ≈

#### 82.980392156863 ≈

#### 82.98

### As a percentage:

#### 82.980392156863 =

#### 82.980392156863 × ^{100}/_{100} =

#### ^{8,298.039215686275}/_{100} =

#### 8,298.039215686275% ≈

#### 8,298.04%

#### 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...