## Reduce: ^{195}/_{187,680}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{195}/_{187,680}

#### The number above the bar is the numerator: 195

#### The number below the bar is the denominator: 187,680

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

^{195}/_{187,680} = 195 ÷ 187,680

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

Value = 195 ÷ 187,680

### 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.

#### 195 = 3 × 5 × 13;

195 is not a prime, is a composite number;

#### 187,680 = 2^{5} × 3 × 5 × 17 × 23;

187,680 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 (195; 187,680) = 3 × 5 = 15

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

^{195}/_{187,680} =

^{(3 × 5 × 13)}/_{(25 × 3 × 5 × 17 × 23)} =

^{((3 × 5 × 13) ÷ (3 × 5))} / _{((25 × 3 × 5 × 17 × 23) ÷ (3 × 5))} =

^{13}/_{(25 × 17 × 23)} =

^{13}/_{12,512}

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

^{13}/_{12,512} 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:

^{13}/_{12,512} =

#### 13 ÷ 12,512 ≈

#### 0.001039002558 ≈

#### 0

### As a percentage:

#### 0.001039002558 =

#### 0.001039002558 × ^{100}/_{100} =

#### ^{0.103900255755}/_{100} =

#### 0.103900255755% ≈

#### 0.1%

#### 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):

^{195}/_{187,680} = ^{13}/_{12,512}

## As a decimal number:

^{195}/_{187,680} ≈ 0.001039002558 ≈ 0

## As a percentage:

^{195}/_{187,680} ≈ 0.1%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions