## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{91,839}/_{55,107}

#### The number above the bar is the numerator: 91,839

#### The number below the bar is the denominator: 55,107

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

^{91,839}/_{55,107} = 91,839 ÷ 55,107

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

Value = 91,839 ÷ 55,107

### 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.

#### 91,839 = 3 × 11^{3} × 23;

91,839 is not a prime, is a composite number;

#### 55,107 = 3^{3} × 13 × 157;

55,107 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 (91,839; 55,107) = 3

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

^{91,839}/_{55,107} =

^{(3 × 113 × 23)}/_{(33 × 13 × 157)} =

^{((3 × 113 × 23) ÷ 3)} / _{((33 × 13 × 157) ÷ 3)} =

^{(113 × 23)}/_{(32 × 13 × 157)} =

^{30,613}/_{18,369}

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

^{30,613}/_{18,369} 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.

#### 30,613 ÷ 18,369 = 1 and remainder = 12,244 =>

#### 30,613 = 1 × 18,369 + 12,244 =>

^{30,613}/_{18,369} =

^{(1 × 18,369 + 12244)} / _{18,369} =

^{(1 × 18,369)} / _{18,369} + ^{12244} / _{18,369} =

#### 1 + ^{12,244}/_{18,369} =

#### 1 ^{12,244}/_{18,369}

### As a decimal number:

#### 1 ^{12,244}/_{18,369} =

#### 1 + ^{12,244}/_{18,369} =

#### 1 + 12,244 ÷ 18,369 ≈

#### 1.666557787577 ≈

#### 1.67

### As a percentage:

#### 1.666557787577 =

#### 1.666557787577 × ^{100}/_{100} =

#### ^{166.65577875769}/_{100} =

#### 166.65577875769% ≈

#### 166.66%

#### 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...