## Reduce: ^{8,324}/_{9,240}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{8,324}/_{9,240}

#### The number above the bar is the numerator: 8,324

#### The number below the bar is the denominator: 9,240

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

^{8,324}/_{9,240} = 8,324 ÷ 9,240

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

Value = 8,324 ÷ 9,240

### 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.

#### 8,324 = 2^{2} × 2,081;

8,324 is not a prime, is a composite number;

#### 9,240 = 2^{3} × 3 × 5 × 7 × 11;

9,240 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 (8,324; 9,240) = 2^{2} = 4

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

^{8,324}/_{9,240} =

^{(22 × 2,081)}/_{(23 × 3 × 5 × 7 × 11)} =

^{((22 × 2,081) ÷ 22)} / _{((23 × 3 × 5 × 7 × 11) ÷ 22)} =

^{2,081}/_{(2 × 3 × 5 × 7 × 11)} =

^{2,081}/_{2,310}

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

^{2,081}/_{2,310} 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:

^{2,081}/_{2,310} =

#### 2,081 ÷ 2,310 ≈

#### 0.900865800866 ≈

#### 0.9

### As a percentage:

#### 0.900865800866 =

#### 0.900865800866 × ^{100}/_{100} =

#### ^{90.08658008658}/_{100} =

#### 90.08658008658% ≈

#### 90.09%

#### 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):

^{8,324}/_{9,240} = ^{2,081}/_{2,310}

## As a decimal number:

^{8,324}/_{9,240} ≈ 0.900865800866 ≈ 0.9

## As a percentage:

^{8,324}/_{9,240} ≈ 90.09%

## More operations of this kind:

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