## Reduce: ^{5,755}/_{2,880}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{5,755}/_{2,880}

#### The number above the bar is the numerator: 5,755

#### The number below the bar is the denominator: 2,880

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

^{5,755}/_{2,880} = 5,755 ÷ 2,880

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

Value = 5,755 ÷ 2,880

### 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.

#### 5,755 = 5 × 1,151;

5,755 is not a prime, is a composite number;

#### 2,880 = 2^{6} × 3^{2} × 5;

2,880 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 (5,755; 2,880) = 5

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

^{5,755}/_{2,880} =

^{(5 × 1,151)}/_{(26 × 32 × 5)} =

^{((5 × 1,151) ÷ 5)} / _{((26 × 32 × 5) ÷ 5)} =

^{1,151}/_{(26 × 32)} =

^{1,151}/_{576}

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

^{1,151}/_{576} 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.

#### 1,151 ÷ 576 = 1 and remainder = 575 =>

#### 1,151 = 1 × 576 + 575 =>

^{1,151}/_{576} =

^{(1 × 576 + 575)} / _{576} =

^{(1 × 576)} / _{576} + ^{575} / _{576} =

#### 1 + ^{575}/_{576} =

#### 1 ^{575}/_{576}

### As a decimal number:

#### 1 ^{575}/_{576} =

#### 1 + ^{575}/_{576} =

#### 1 + 575 ÷ 576 ≈

#### 1.998263888889 ≈

#### 2

### As a percentage:

#### 1.998263888889 =

#### 1.998263888889 × ^{100}/_{100} =

#### ^{199.826388888889}/_{100} =

#### 199.826388888889% ≈

#### 199.83%

#### 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):

^{5,755}/_{2,880} = ^{1,151}/_{576}

## As a mixed number (mixed fraction)

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

^{5,755}/_{2,880} = 1 ^{575}/_{576}

## As a decimal number:

^{5,755}/_{2,880} ≈ 1.998263888889 ≈ 2

## As a percentage:

^{5,755}/_{2,880} ≈ 199.83%

## More operations of this kind:

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