## Reduce: ^{1,440}/_{756}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{1,440}/_{756}

#### The number above the bar is the numerator: 1,440

#### The number below the bar is the denominator: 756

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

^{1,440}/_{756} = 1,440 ÷ 756

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

Value = 1,440 ÷ 756

### 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.

#### 1,440 = 2^{5} × 3^{2} × 5;

1,440 is not a prime, is a composite number;

#### 756 = 2^{2} × 3^{3} × 7;

756 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 (1,440; 756) = 2^{2} × 3^{2} = 36

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

^{1,440}/_{756} =

^{(25 × 32 × 5)}/_{(22 × 33 × 7)} =

^{((25 × 32 × 5) ÷ (22 × 32))} / _{((22 × 33 × 7) ÷ (22 × 32))} =

^{(23 × 5)}/_{(3 × 7)} =

^{40}/_{21}

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

^{40}/_{21} 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.

#### 40 ÷ 21 = 1 and remainder = 19 =>

#### 40 = 1 × 21 + 19 =>

^{40}/_{21} =

^{(1 × 21 + 19)} / _{21} =

^{(1 × 21)} / _{21} + ^{19} / _{21} =

#### 1 + ^{19}/_{21} =

#### 1 ^{19}/_{21}

### As a decimal number:

#### 1 ^{19}/_{21} =

#### 1 + ^{19}/_{21} =

#### 1 + 19 ÷ 21 ≈

#### 1.904761904762 ≈

#### 1.9

### As a percentage:

#### 1.904761904762 =

#### 1.904761904762 × ^{100}/_{100} =

#### ^{190.476190476191}/_{100} =

#### 190.476190476191% ≈

#### 190.48%

#### 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):

^{1,440}/_{756} = ^{40}/_{21}

## As a mixed number (mixed fraction)

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

^{1,440}/_{756} = 1 ^{19}/_{21}

## As a decimal number:

^{1,440}/_{756} ≈ 1.904761904762 ≈ 1.9

## As a percentage:

^{1,440}/_{756} ≈ 190.48%

## More operations of this kind:

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