## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{107,058}/_{53,793}

#### The number above the bar is the numerator: 107,058

#### The number below the bar is the denominator: 53,793

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

^{107,058}/_{53,793} = 107,058 ÷ 53,793

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

Value = 107,058 ÷ 53,793

### 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.

#### 107,058 = 2 × 3 × 7 × 2,549;

107,058 is not a prime, is a composite number;

#### 53,793 = 3^{2} × 43 × 139;

53,793 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 (107,058; 53,793) = 3

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

^{107,058}/_{53,793} =

^{(2 × 3 × 7 × 2,549)}/_{(32 × 43 × 139)} =

^{((2 × 3 × 7 × 2,549) ÷ 3)} / _{((32 × 43 × 139) ÷ 3)} =

^{(2 × 7 × 2,549)}/_{(3 × 43 × 139)} =

^{35,686}/_{17,931}

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

^{35,686}/_{17,931} 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.

#### 35,686 ÷ 17,931 = 1 and remainder = 17,755 =>

#### 35,686 = 1 × 17,931 + 17,755 =>

^{35,686}/_{17,931} =

^{(1 × 17,931 + 17755)} / _{17,931} =

^{(1 × 17,931)} / _{17,931} + ^{17755} / _{17,931} =

#### 1 + ^{17,755}/_{17,931} =

#### 1 ^{17,755}/_{17,931}

### As a decimal number:

#### 1 ^{17,755}/_{17,931} =

#### 1 + ^{17,755}/_{17,931} =

#### 1 + 17,755 ÷ 17,931 ≈

#### 1.990184596509 ≈

#### 1.99

### As a percentage:

#### 1.990184596509 =

#### 1.990184596509 × ^{100}/_{100} =

#### ^{199.018459650884}/_{100} =

#### 199.018459650884% ≈

#### 199.02%

#### 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...