## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{9,454}/_{14}

#### The number above the bar is the numerator: 9,454

#### The number below the bar is the denominator: 14

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

^{9,454}/_{14} = 9,454 ÷ 14

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

Value = 9,454 ÷ 14

### 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.

#### 9,454 = 2 × 29 × 163;

9,454 is not a prime, is a composite number;

#### 14 = 2 × 7;

14 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 (9,454; 14) = 2

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

^{9,454}/_{14} =

^{(2 × 29 × 163)}/_{(2 × 7)} =

^{((2 × 29 × 163) ÷ 2)} / _{((2 × 7) ÷ 2)} =

^{(29 × 163)}/_{7} =

^{4,727}/_{7}

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

^{4,727}/_{7} 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.

#### 4,727 ÷ 7 = 675 and remainder = 2 =>

#### 4,727 = 675 × 7 + 2 =>

^{4,727}/_{7} =

^{(675 × 7 + 2)} / _{7} =

^{(675 × 7)} / _{7} + ^{2} / _{7} =

#### 675 + ^{2}/_{7} =

#### 675 ^{2}/_{7}

### As a decimal number:

#### 675 ^{2}/_{7} =

#### 675 + ^{2}/_{7} =

#### 675 + 2 ÷ 7 ≈

#### 675.285714285714 ≈

#### 675.29

### As a percentage:

#### 675.285714285714 =

#### 675.285714285714 × ^{100}/_{100} =

#### ^{67,528.571428571429}/_{100} =

#### 67,528.571428571429% ≈

#### 67,528.57%

#### 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...