## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{10,395,000,002}/_{24}

#### The number above the bar is the numerator: 10,395,000,002

#### The number below the bar is the denominator: 24

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

^{10,395,000,002}/_{24} = 10,395,000,002 ÷ 24

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

Value = 10,395,000,002 ÷ 24

### 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.

#### 10,395,000,002 = 2 × 37 × 140,472,973;

10,395,000,002 is not a prime, is a composite number;

#### 24 = 2^{3} × 3;

24 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 (10,395,000,002; 24) = 2

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

^{10,395,000,002}/_{24} =

^{(2 × 37 × 140,472,973)}/_{(23 × 3)} =

^{((2 × 37 × 140,472,973) ÷ 2)} / _{((23 × 3) ÷ 2)} =

^{(37 × 140,472,973)}/_{(22 × 3)} =

^{5,197,500,001}/_{12}

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

^{5,197,500,001}/_{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.

#### 5,197,500,001 ÷ 12 = 433,125,000 and remainder = 1 =>

#### 5,197,500,001 = 433,125,000 × 12 + 1 =>

^{5,197,500,001}/_{12} =

^{(433,125,000 × 12 + 1)} / _{12} =

^{(433,125,000 × 12)} / _{12} + ^{1} / _{12} =

#### 433,125,000 + ^{1}/_{12} =

#### 433,125,000 ^{1}/_{12}

### As a decimal number:

#### 433,125,000 ^{1}/_{12} =

#### 433,125,000 + ^{1}/_{12} =

#### 433,125,000 + 1 ÷ 12 ≈

#### 433,125,000.083333333333 ≈

#### 433,125,000.08

### As a percentage:

#### 433,125,000.083333333333 =

#### 433,125,000.083333333333 × ^{100}/_{100} =

#### ^{43,312,500,008.333333333333}/_{100} =

#### 43,312,500,008.333333333333% ≈

#### 43,312,500,008.33%

#### 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...