## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{113,902}/_{44}

#### The number above the bar is the numerator: 113,902

#### The number below the bar is the denominator: 44

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

^{113,902}/_{44} = 113,902 ÷ 44

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

Value = 113,902 ÷ 44

### 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.

#### 113,902 = 2 × 56,951;

113,902 is not a prime, is a composite number;

#### 44 = 2^{2} × 11;

44 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 (113,902; 44) = 2

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

^{113,902}/_{44} =

^{(2 × 56,951)}/_{(22 × 11)} =

^{((2 × 56,951) ÷ 2)} / _{((22 × 11) ÷ 2)} =

^{56,951}/_{(2 × 11)} =

^{56,951}/_{22}

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

^{56,951}/_{22} 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.

#### 56,951 ÷ 22 = 2,588 and remainder = 15 =>

#### 56,951 = 2,588 × 22 + 15 =>

^{56,951}/_{22} =

^{(2,588 × 22 + 15)} / _{22} =

^{(2,588 × 22)} / _{22} + ^{15} / _{22} =

#### 2,588 + ^{15}/_{22} =

#### 2,588 ^{15}/_{22}

### As a decimal number:

#### 2,588 ^{15}/_{22} =

#### 2,588 + ^{15}/_{22} =

#### 2,588 + 15 ÷ 22 ≈

#### 2,588.681818181818 ≈

#### 2,588.68

### As a percentage:

#### 2,588.681818181818 =

#### 2,588.681818181818 × ^{100}/_{100} =

#### ^{258,868.181818181818}/_{100} =

#### 258,868.181818181818% ≈

#### 258,868.18%

#### 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...