## Reduce: ^{5,465}/_{76}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{5,465}/_{76}

#### The number above the bar is the numerator: 5,465

#### The number below the bar is the denominator: 76

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

^{5,465}/_{76} = 5,465 ÷ 76

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

Value = 5,465 ÷ 76

### 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.

#### 5,465 = 5 × 1,093;

5,465 is not a prime, is a composite number;

#### 76 = 2^{2} × 19;

76 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 (5,465; 76) = 1

coprime numbers (relatively prime)

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

^{5,465}/_{76} 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.

#### 5,465 ÷ 76 = 71 and remainder = 69 =>

#### 5,465 = 71 × 76 + 69 =>

^{5,465}/_{76} =

^{(71 × 76 + 69)} / _{76} =

^{(71 × 76)} / _{76} + ^{69} / _{76} =

#### 71 + ^{69}/_{76} =

#### 71 ^{69}/_{76}

### As a decimal number:

#### 71 ^{69}/_{76} =

#### 71 + ^{69}/_{76} =

#### 71 + 69 ÷ 76 ≈

#### 71.907894736842 ≈

#### 71.91

### As a percentage:

#### 71.907894736842 =

#### 71.907894736842 × ^{100}/_{100} =

#### ^{7,190.789473684211}/_{100} =

#### 7,190.789473684211% ≈

#### 7,190.79%

#### 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):

^{5,465}/_{76} = ^{5,465}/_{76}

## As a mixed number (mixed fraction)

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

^{5,465}/_{76} = 71 ^{69}/_{76}

## As a decimal number:

^{5,465}/_{76} ≈ 71.907894736842 ≈ 71.91

## As a percentage:

^{5,465}/_{76} ≈ 7,190.79%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions