## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{95,631}/_{12}

#### The number above the bar is the numerator: 95,631

#### The number below the bar is the denominator: 12

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

^{95,631}/_{12} = 95,631 ÷ 12

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

Value = 95,631 ÷ 12

### 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.

#### 95,631 = 3 × 127 × 251;

95,631 is not a prime, is a composite number;

#### 12 = 2^{2} × 3;

12 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 (95,631; 12) = 3

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

^{95,631}/_{12} =

^{(3 × 127 × 251)}/_{(22 × 3)} =

^{((3 × 127 × 251) ÷ 3)} / _{((22 × 3) ÷ 3)} =

^{(127 × 251)}/_{22} =

^{31,877}/_{4}

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

^{31,877}/_{4} 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.

#### 31,877 ÷ 4 = 7,969 and remainder = 1 =>

#### 31,877 = 7,969 × 4 + 1 =>

^{31,877}/_{4} =

^{(7,969 × 4 + 1)} / _{4} =

^{(7,969 × 4)} / _{4} + ^{1} / _{4} =

#### 7,969 + ^{1}/_{4} =

#### 7,969 ^{1}/_{4}

### As a decimal number:

#### 7,969 ^{1}/_{4} =

#### 7,969 + ^{1}/_{4} =

#### 7,969 + 1 ÷ 4 =

#### 7,969.25

### As a percentage:

#### 7,969.25 =

#### 7,969.25 × ^{100}/_{100} =

#### ^{796,925}/_{100} =

#### 796,925%

#### 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...