## Reduce: ^{19}/_{4}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{19}/_{4}

#### The number above the bar is the numerator: 19

#### The number below the bar is the denominator: 4

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

^{19}/_{4} = 19 ÷ 4

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

Value = 19 ÷ 4

### 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.

#### 19 is a prime number, it cannot be broken down to other prime factors;

#### 4 = 2^{2};

4 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).

#### But the two numbers have no common prime factors.

#### gcf, hcf, gcd (19; 4) = 1

coprime numbers (relatively prime)

## Fraction's numerator and denominator are coprime numbers (no common prime factors). Fraction cannot be reduced (simplified) - irreducible.

^{19}/_{4} is an improper fraction.

#### An improper fraction: numerator larger than denominator.

## 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.

#### 19 ÷ 4 = 4 and remainder = 3 =>

#### 19 = 4 × 4 + 3 =>

^{19}/_{4} =

^{(4 × 4 + 3)} / _{4} =

^{(4 × 4)} / _{4} + ^{3} / _{4} =

#### 4 + ^{3}/_{4} =

#### 4 ^{3}/_{4}

### As a decimal number:

#### 4 ^{3}/_{4} =

#### 4 + ^{3}/_{4} =

#### 4 + 3 ÷ 4 =

#### 4.75

### As a percentage:

#### 4.75 =

#### 4.75 × ^{100}/_{100} =

#### ^{475}/_{100} =

#### 475%

#### 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 four ways ::

## As an improper fraction

(numerator larger than denominator):

^{19}/_{4} = ^{19}/_{4}

## As a mixed number (mixed fraction)

(a whole number and a proper fraction, of the same sign):

^{19}/_{4} = 4 ^{3}/_{4}

## As a decimal number:

^{19}/_{4} = 4.75

## As a percentage:

^{19}/_{4} = 475%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions