## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{1,700}/_{20,000}

#### The number above the bar is the numerator: 1,700

#### The number below the bar is the denominator: 20,000

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

^{1,700}/_{20,000} = 1,700 ÷ 20,000

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

Value = 1,700 ÷ 20,000

### 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.

#### 1,700 = 2^{2} × 5^{2} × 17;

1,700 is not a prime, is a composite number;

#### 20,000 = 2^{5} × 5^{4};

20,000 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 (1,700; 20,000) = 2^{2} × 5^{2} = 100

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

^{1,700}/_{20,000} =

^{(22 × 52 × 17)}/_{(25 × 54)} =

^{((22 × 52 × 17) ÷ (22 × 52))} / _{((25 × 54) ÷ (22 × 52))} =

^{17}/_{(23 × 52)} =

^{17}/_{200}

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

^{17}/_{200} is a proper fraction.

#### A proper fraction: numerator smaller than denominator.

## Rewrite the end result, continued below...

## Rewrite the end result:

### As a decimal number:

^{17}/_{200} =

#### 17 ÷ 200 =

#### 0.085 ≈

#### 0.09

### As a percentage:

#### 0.085 =

#### 0.085 × ^{100}/_{100} =

#### ^{8.5}/_{100} =

#### 8.5%

#### 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...