## Reduce: ^{1,135}/_{390}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{1,135}/_{390}

#### The number above the bar is the numerator: 1,135

#### The number below the bar is the denominator: 390

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

^{1,135}/_{390} = 1,135 ÷ 390

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

Value = 1,135 ÷ 390

### 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.

#### 1,135 = 5 × 227;

1,135 is not a prime, is a composite number;

#### 390 = 2 × 3 × 5 × 13;

390 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 (1,135; 390) = 5

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

^{1,135}/_{390} =

^{(5 × 227)}/_{(2 × 3 × 5 × 13)} =

^{((5 × 227) ÷ 5)} / _{((2 × 3 × 5 × 13) ÷ 5)} =

^{227}/_{(2 × 3 × 13)} =

^{227}/_{78}

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

^{227}/_{78} 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.

#### 227 ÷ 78 = 2 and remainder = 71 =>

#### 227 = 2 × 78 + 71 =>

^{227}/_{78} =

^{(2 × 78 + 71)} / _{78} =

^{(2 × 78)} / _{78} + ^{71} / _{78} =

#### 2 + ^{71}/_{78} =

#### 2 ^{71}/_{78}

### As a decimal number:

#### 2 ^{71}/_{78} =

#### 2 + ^{71}/_{78} =

#### 2 + 71 ÷ 78 ≈

#### 2.910256410256 ≈

#### 2.91

### As a percentage:

#### 2.910256410256 =

#### 2.910256410256 × ^{100}/_{100} =

#### ^{291.025641025641}/_{100} =

#### 291.025641025641% ≈

#### 291.03%

#### 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):

^{1,135}/_{390} = ^{227}/_{78}

## As a mixed number (mixed fraction)

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

^{1,135}/_{390} = 2 ^{71}/_{78}

## As a decimal number:

^{1,135}/_{390} ≈ 2.910256410256 ≈ 2.91

## As a percentage:

^{1,135}/_{390} ≈ 291.03%

## More operations of this kind:

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