## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{31,983}/_{9}

#### The number above the bar is the numerator: 31,983

#### The number below the bar is the denominator: 9

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

^{31,983}/_{9} = 31,983 ÷ 9

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

Value = 31,983 ÷ 9

### 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.

#### 31,983 = 3 × 7 × 1,523;

31,983 is not a prime, is a composite number;

#### 9 = 3^{2};

9 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 (31,983; 9) = 3

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

^{31,983}/_{9} =

^{(3 × 7 × 1,523)}/_{32} =

^{((3 × 7 × 1,523) ÷ 3)} / _{(32 ÷ 3)} =

^{(7 × 1,523)}/_{3} =

^{10,661}/_{3}

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

^{10,661}/_{3} 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.

#### 10,661 ÷ 3 = 3,553 and remainder = 2 =>

#### 10,661 = 3,553 × 3 + 2 =>

^{10,661}/_{3} =

^{(3,553 × 3 + 2)} / _{3} =

^{(3,553 × 3)} / _{3} + ^{2} / _{3} =

#### 3,553 + ^{2}/_{3} =

#### 3,553 ^{2}/_{3}

### As a decimal number:

#### 3,553 ^{2}/_{3} =

#### 3,553 + ^{2}/_{3} =

#### 3,553 + 2 ÷ 3 ≈

#### 3,553.666666666667 ≈

#### 3,553.67

### As a percentage:

#### 3,553.666666666667 =

#### 3,553.666666666667 × ^{100}/_{100} =

#### ^{355,366.666666666667}/_{100} =

#### 355,366.666666666667% ≈

#### 355,366.67%

#### 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...