## Reduce: ^{200}/_{135,915}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{200}/_{135,915}

#### The number above the bar is the numerator: 200

#### The number below the bar is the denominator: 135,915

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

^{200}/_{135,915} = 200 ÷ 135,915

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

Value = 200 ÷ 135,915

### 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.

#### 200 = 2^{3} × 5^{2};

200 is not a prime, is a composite number;

#### 135,915 = 3 × 5 × 13 × 17 × 41;

135,915 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 (200; 135,915) = 5

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

^{200}/_{135,915} =

^{(23 × 52)}/_{(3 × 5 × 13 × 17 × 41)} =

^{((23 × 52) ÷ 5)} / _{((3 × 5 × 13 × 17 × 41) ÷ 5)} =

^{(23 × 5)}/_{(3 × 13 × 17 × 41)} =

^{40}/_{27,183}

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

^{40}/_{27,183} 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:

^{40}/_{27,183} =

#### 40 ÷ 27,183 ≈

#### 0.001471507928 ≈

#### 0

### As a percentage:

#### 0.001471507928 =

#### 0.001471507928 × ^{100}/_{100} =

#### ^{0.147150792775}/_{100} =

#### 0.147150792775% ≈

#### 0.15%

#### 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...

## Final answer:

:: written in three ways ::

## As a proper fraction

(numerator smaller than denominator):

^{200}/_{135,915} = ^{40}/_{27,183}

## As a decimal number:

^{200}/_{135,915} ≈ 0.001471507928 ≈ 0

## As a percentage:

^{200}/_{135,915} ≈ 0.15%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions