## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{1,209}/_{8}

#### The number above the bar is the numerator: 1,209

#### The number below the bar is the denominator: 8

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

^{1,209}/_{8} = 1,209 ÷ 8

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

Value = 1,209 ÷ 8

### 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.

### Integer numbers prime factorization:

#### Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

#### 1,209 = 3 × 13 × 31;

1,209 is not a prime, is a composite number;

#### 8 = 2^{3};

8 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 (1,209; 8) = 1

coprime numbers (relatively prime)

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

^{1,209}/_{8} 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.

#### 1,209 ÷ 8 = 151 and remainder = 1 =>

#### 1,209 = 151 × 8 + 1 =>

^{1,209}/_{8} =

^{(151 × 8 + 1)} / _{8} =

^{(151 × 8)} / _{8} + ^{1} / _{8} =

#### 151 + ^{1}/_{8} =

#### 151 ^{1}/_{8}

### As a decimal number:

#### 151 ^{1}/_{8} =

#### 151 + ^{1}/_{8} =

#### 151 + 1 ÷ 8 =

#### 151.125 ≈

#### 151.13

### As a percentage:

#### 151.125 =

#### 151.125 × ^{100}/_{100} =

#### ^{15,112.5}/_{100} =

#### 15,112.5%

#### 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...